fiveworlds

That governments need to be stricter with such things. If we go to the trouble of developing a vaccine for an illness then we should vaccinate everybody against the disease in the hopes of killing it off for good and currently infected people should be quarantined from the rest of the general population until such a time as they are free from the risk of infecting others. If we only vaccinate some people the illness could mutate and become immune to that method of vaccination. The main problem with such a method is it would require fairly synchronized vaccination everywhere on earth.

Lots of maths problems have been solved through arithmetic. It is important to note though that because we can solve it with a computer we can't verify that a solution is correct in either way on a computer.

One of the main problems with proving riemann in either way is that modern computers do not reliably compute floating point numbers to any degree of accuracy. If you wanted to really prove it you have to do the calculations by hand.

If only it were that easy. I generally only take the bare minimum I need my phone and wallet to get home so I don't have a choice about bringing them. Then there's the times where bags are just left on the ground in or outside the exam hall and it makes me just as uncomfortable because nothing would stop a student or teacher from picking up my bag and just walking out with it.

In the room outside the exam hall which in my opinion makes it soo easy for somebody to steal. I really don't trust people as far as I can throw them.

Hey, college exams are really strict in that they force you to hand them your phone, wallet etc to stop cheating. While I can understand where they are coming from am I the only one here that feels uncomfortable with handing their important personal belongings to people they don't know?

I dunno where you are getting that from if you refer to the paper where non-determinism is defined the guy who created NDTM mentioned that all nondeterministic turing machines can be simulated by more complicated deterministic turing machines. So all NP problems have to run on non-deterministic turing machines. They aren't sure if we can make deterministic machines run as fast as non-deterministic machines but I am fairly certain that we can. Consider that NDTM can move either left or right. We know from work on colossus that just moving one direction is fastest. Also the other property of a non-deterministic turing machine is the ability to replace a string with any of an array of strings. We can define a DTM that does the same thing with multiple tapes. So to give an example of a DTM using mutiple tape copy operation. var a = ['a','b','c'] for(i = 0; i < a.length; i = i + 1) { } We have 2 tapes there 1 to store the index and 1 to store the array. When using a non-deterministic idea the array is hard coded and not in memory. The only time it is ever really used now is in read only memory for the bios. The paper was written around the time that ROM was invented. EPROM is deterministic. If we have an instruction say a replace with b we can now do what they couldn't do 50 years ago and change b to c. Now we get wikipedia's definition There's basically no difference between the a non-deterministic turing machine and a deterministic turing machine anymore. Once you have the actual definition all the wiki's are just weird and confusing and claymath's paper is just as bad. You'd need to just take a red pen and mark out every single mistake they made and there is so many.

It'll take O(1) space too since if we make a circuit to solve it we can't go about changing it at runtime. Also my argument has always been that non-determinism doesn't provide any speed increase to solving any of the problems. The real definition for non-determinism can be found in the paper where it was originally defined http://www.cse.chalmers.se/~coquand/AUTOMATA/rs.pdf Also we can show that it isn't in np because it is not easy to verify as if I said a number was the minimum you would still need to do k! checks to prove it was the minimum. Similarly for boolean sat you couldn't say oh this is false because if a = 0 and b =0 then it is false because a = 1 and b =1 might be true.

I was asked to make an algorithm for TSP in determinstic polynomial time. input = list of cities and their distances of length n. Each city is seperated by a space e.g. "distance,distance,distance distance,distance,distance distance,distance,distance" k = number of cities = found by reading k distances. we populate strings t[] of length k on k! tapes containing all instaces of k! 0000,0001 etc by reading string of length n; each t[] is replaced by string index; 0214 = cities[0][0] cities[1][2] cities[2][1] cities[3][4]. replace all t[] with their sum which is equivalent to the distances between the cities. find the minimum of t[]; finding k takes O(k) time. making t[] and replacing all t[] with their sum takes O(n) time but O(k!) space; finding the minimum of t[] takes O(k!) time; Therefore the runtime of TSP is (n + k!) since n can be 1 we can change this to k!. So TSP is reducible to finding the minimum of a list of numbers. We can find the minimum of 2 numbers with combinatorial logic and by extension we can find the minimum value of k! numbers with combinatorial logic in O(1) time. Therefore TSP is reducible to O(1) time in deterministic polynomial time. On modern computers we are limited by the von neumann bottleneck etc so the best runtime on a normal computer would be k! since we can only do one if( a < b) at a time if we could do it if(a < b < c) then it would half the runtime.

https://en.wikipedia.org/wiki/Boolean_satisfiability_problem I mean the boolean satisfiability problem as we can see from the Deterministic Turing Macine Finite State Machine State Configuration Table below we need only one movement from right to left to run the last equation. There it has a worst case runtime of O(N) which can be simplified to O(1) with a reader that can read strings of size n. Since the states for strings are fairly complicated as in millions of possibilities I'll just use a shorthand arrow notation. A -> last index of !A etc. The main reasoning behind it is that all logic gates can be represented by NAND gates and NAND gates can be represented as NOT(A AND B). Which left me to conclude that the only time a circuit is always false is in instances where A AND NOT A are in the same circuit and all the circuits between them automatically become false as a result. So if I find the last instance where it is always false and it has a ! then it can be true for instance (((A AND NOT B) AND (A AND B))!). Then you need to count all the NOT gates between that instance and the output and it flips between true and false which is basically just odd or even. Also you are not allowed to use !(A and A) to make a different circuit that is always false since it can be simulated using one !.

Then why are you talking about it? I thought up of a much faster algorithm for boolean sat. <script> var str = "((((((((A and B)AND(A and !B))AND(!A and B))!AND(A and A))AND(A and !B))!)AND(A and !B))!)"; var letters = ['A','B'], lastIndex = 0, countright = 0, satisfiability = ['false','true']; for(var i = 0; i < letters.length; i = i + 1){ if((str.lastIndexOf(letters[i]) !=-1) && (str.lastIndexOf("!"+letters[i]) != -1)){ if(str.lastIndexOf("!"+letters[i])>str.lastIndexOf(letters[i])){ if(lastIndex < str.lastIndexOf(letters[i])) { lastIndex = str.lastIndexOf(letters[i]); satisfiability = ['false','true'] }; } else if (lastIndex < str.lastIndexOf("!"+letters[i])){ lastIndex = str.lastIndexOf("!"+letters[i]); satisfiability = ['false','true'] } if(str.lastIndexOf(letters[i]+" AND " + letters[i]) > lastIndex){ lastIndex = str.lastIndexOf(letters[i]+" AND " + letters[i]); satisfiability = ['true','false']; } } } while(countright < 2){ if(str.charAt(lastIndex)==')'){countright = countright + 1;} lastIndex = lastIndex + 1; } str = str.substr(lastIndex - 1); var count = str.length; while(str.indexOf(")!)") != -1) { str = str.replace(")!)","))"); } count = count - str.length; document.write((count % 2 == 0)? satisfiability[0] : satisfiability[1]); </script>

We can actually generate the O(1) equation for the above now it is. var booleanExpression = "(((a AND a) AND !(a AND a)) AND ((a AND a) AND !(a AND a)))"; for(var i = 0; i < 4; i = i +1){ booleanExpression = booleanExpression.replace('(a AND !a)','false').replace('(a AND a)','true').replace('(a AND b)','true').replace('(a AND c)','true').replace('(a AND d)','true').replace('(a AND e)','true').replace('(a AND f)','true').replace('(a AND g)','true').replace('(a AND i)','true').replace('(a AND h)','true').replace('(a AND j)','true').replace('(a AND k)','true').replace('(a AND l)','true').replace('(a AND m)','true').replace('(a AND n)','true').replace('(a AND o)','true').replace('(a AND p)','true').replace('(a AND q)','true').replace('(a AND r)','true').replace('(a AND s)','true').replace('(a AND t)','true').replace('(a AND u)','true').replace('(a AND v)','true').replace('(a AND w)','true').replace('(a AND x)','true').replace('(a AND y)','true').replace('(a AND z)','true').replace('(!a AND a)','false').replace('(a AND !a)','true').replace('(!a AND !a)','true').replace('!(a AND !a)','true').replace('!(!a AND !a)','true').replace('!(a AND !a)','true').replace('!(!a AND !a)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(b AND !b)','false').replace('(b AND a)','true').replace('(b AND b)','true').replace('(b AND c)','true').replace('(b AND d)','true').replace('(b AND e)','true').replace('(b AND f)','true').replace('(b AND g)','true').replace('(b AND i)','true').replace('(b AND h)','true').replace('(b AND j)','true').replace('(b AND k)','true').replace('(b AND l)','true').replace('(b AND m)','true').replace('(b AND n)','true').replace('(b AND o)','true').replace('(b AND p)','true').replace('(b AND q)','true').replace('(b AND r)','true').replace('(b AND s)','true').replace('(b AND t)','true').replace('(b AND u)','true').replace('(b AND v)','true').replace('(b AND w)','true').replace('(b AND x)','true').replace('(b AND y)','true').replace('(b AND z)','true').replace('(!b AND b)','false').replace('(b AND !b)','true').replace('(!b AND !b)','true').replace('!(b AND !b)','true').replace('!(!b AND !b)','true').replace('!(b AND !b)','true').replace('!(!b AND !b)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(c AND !c)','false').replace('(c AND a)','true').replace('(c AND b)','true').replace('(c AND c)','true').replace('(c AND d)','true').replace('(c AND e)','true').replace('(c AND f)','true').replace('(c AND g)','true').replace('(c AND i)','true').replace('(c AND h)','true').replace('(c AND j)','true').replace('(c AND k)','true').replace('(c AND l)','true').replace('(c AND m)','true').replace('(c AND n)','true').replace('(c AND o)','true').replace('(c AND p)','true').replace('(c AND q)','true').replace('(c AND r)','true').replace('(c AND s)','true').replace('(c AND t)','true').replace('(c AND u)','true').replace('(c AND v)','true').replace('(c AND w)','true').replace('(c AND x)','true').replace('(c AND y)','true').replace('(c AND z)','true').replace('(!c AND c)','false').replace('(c AND !c)','true').replace('(!c AND !c)','true').replace('!(c AND !c)','true').replace('!(!c AND !c)','true').replace('!(c AND !c)','true').replace('!(!c AND !c)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(d AND !d)','false').replace('(d AND a)','true').replace('(d AND b)','true').replace('(d AND c)','true').replace('(d AND d)','true').replace('(d AND e)','true').replace('(d AND f)','true').replace('(d AND g)','true').replace('(d AND i)','true').replace('(d AND h)','true').replace('(d AND j)','true').replace('(d AND k)','true').replace('(d AND l)','true').replace('(d AND m)','true').replace('(d AND n)','true').replace('(d AND o)','true').replace('(d AND p)','true').replace('(d AND q)','true').replace('(d AND r)','true').replace('(d AND s)','true').replace('(d AND t)','true').replace('(d AND u)','true').replace('(d AND v)','true').replace('(d AND w)','true').replace('(d AND x)','true').replace('(d AND y)','true').replace('(d AND z)','true').replace('(!d AND d)','false').replace('(d AND !d)','true').replace('(!d AND !d)','true').replace('!(d AND !d)','true').replace('!(!d AND !d)','true').replace('!(d AND !d)','true').replace('!(!d AND !d)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(e AND !e)','false').replace('(e AND a)','true').replace('(e AND b)','true').replace('(e AND c)','true').replace('(e AND d)','true').replace('(e AND e)','true').replace('(e AND f)','true').replace('(e AND g)','true').replace('(e AND i)','true').replace('(e AND h)','true').replace('(e AND j)','true').replace('(e AND k)','true').replace('(e AND l)','true').replace('(e AND m)','true').replace('(e AND n)','true').replace('(e AND o)','true').replace('(e AND p)','true').replace('(e AND q)','true').replace('(e AND r)','true').replace('(e AND s)','true').replace('(e AND t)','true').replace('(e AND u)','true').replace('(e AND v)','true').replace('(e AND w)','true').replace('(e AND x)','true').replace('(e AND y)','true').replace('(e AND z)','true').replace('(!e AND e)','false').replace('(e AND !e)','true').replace('(!e AND !e)','true').replace('!(e AND !e)','true').replace('!(!e AND !e)','true').replace('!(e AND !e)','true').replace('!(!e AND !e)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(f AND !f)','false').replace('(f AND a)','true').replace('(f AND b)','true').replace('(f AND c)','true').replace('(f AND d)','true').replace('(f AND e)','true').replace('(f AND f)','true').replace('(f AND g)','true').replace('(f AND i)','true').replace('(f AND h)','true').replace('(f AND j)','true').replace('(f AND k)','true').replace('(f AND l)','true').replace('(f AND m)','true').replace('(f AND n)','true').replace('(f AND o)','true').replace('(f AND p)','true').replace('(f AND q)','true').replace('(f AND r)','true').replace('(f AND s)','true').replace('(f AND t)','true').replace('(f AND u)','true').replace('(f AND v)','true').replace('(f AND w)','true').replace('(f AND x)','true').replace('(f AND y)','true').replace('(f AND z)','true').replace('(!f AND f)','false').replace('(f AND !f)','true').replace('(!f AND !f)','true').replace('!(f AND !f)','true').replace('!(!f AND !f)','true').replace('!(f AND !f)','true').replace('!(!f AND !f)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(g AND !g)','false').replace('(g AND a)','true').replace('(g AND b)','true').replace('(g AND c)','true').replace('(g AND d)','true').replace('(g AND e)','true').replace('(g AND f)','true').replace('(g AND g)','true').replace('(g AND i)','true').replace('(g AND h)','true').replace('(g AND j)','true').replace('(g AND k)','true').replace('(g AND l)','true').replace('(g AND m)','true').replace('(g AND n)','true').replace('(g AND o)','true').replace('(g AND p)','true').replace('(g AND q)','true').replace('(g AND r)','true').replace('(g AND s)','true').replace('(g AND t)','true').replace('(g AND u)','true').replace('(g AND v)','true').replace('(g AND w)','true').replace('(g AND x)','true').replace('(g AND y)','true').replace('(g AND z)','true').replace('(!g AND g)','false').replace('(g AND !g)','true').replace('(!g AND !g)','true').replace('!(g AND !g)','true').replace('!(!g AND !g)','true').replace('!(g AND !g)','true').replace('!(!g AND !g)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(i AND !i)','false').replace('(i AND a)','true').replace('(i AND b)','true').replace('(i AND c)','true').replace('(i AND d)','true').replace('(i AND e)','true').replace('(i AND f)','true').replace('(i AND g)','true').replace('(i AND i)','true').replace('(i AND h)','true').replace('(i AND j)','true').replace('(i AND k)','true').replace('(i AND l)','true').replace('(i AND m)','true').replace('(i AND n)','true').replace('(i AND o)','true').replace('(i AND p)','true').replace('(i AND q)','true').replace('(i AND r)','true').replace('(i AND s)','true').replace('(i AND t)','true').replace('(i AND u)','true').replace('(i AND v)','true').replace('(i AND w)','true').replace('(i AND x)','true').replace('(i AND y)','true').replace('(i AND z)','true').replace('(!i AND i)','false').replace('(i AND !i)','true').replace('(!i AND !i)','true').replace('!(i AND !i)','true').replace('!(!i AND !i)','true').replace('!(i AND !i)','true').replace('!(!i AND !i)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(h AND !h)','false').replace('(h AND a)','true').replace('(h AND b)','true').replace('(h AND c)','true').replace('(h AND d)','true').replace('(h AND e)','true').replace('(h AND f)','true').replace('(h AND g)','true').replace('(h AND i)','true').replace('(h AND h)','true').replace('(h AND j)','true').replace('(h AND k)','true').replace('(h AND l)','true').replace('(h AND m)','true').replace('(h AND n)','true').replace('(h AND o)','true').replace('(h AND p)','true').replace('(h AND q)','true').replace('(h AND r)','true').replace('(h AND s)','true').replace('(h AND t)','true').replace('(h AND u)','true').replace('(h AND v)','true').replace('(h AND w)','true').replace('(h AND x)','true').replace('(h AND y)','true').replace('(h AND z)','true').replace('(!h AND h)','false').replace('(h AND !h)','true').replace('(!h AND !h)','true').replace('!(h AND !h)','true').replace('!(!h AND !h)','true').replace('!(h AND !h)','true').replace('!(!h AND !h)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(j AND !j)','false').replace('(j AND a)','true').replace('(j AND b)','true').replace('(j AND c)','true').replace('(j AND d)','true').replace('(j AND e)','true').replace('(j AND f)','true').replace('(j AND g)','true').replace('(j AND i)','true').replace('(j AND h)','true').replace('(j AND j)','true').replace('(j AND k)','true').replace('(j AND l)','true').replace('(j AND m)','true').replace('(j AND n)','true').replace('(j AND o)','true').replace('(j AND p)','true').replace('(j AND q)','true').replace('(j AND r)','true').replace('(j AND s)','true').replace('(j AND t)','true').replace('(j AND u)','true').replace('(j AND v)','true').replace('(j AND w)','true').replace('(j AND x)','true').replace('(j AND y)','true').replace('(j AND z)','true').replace('(!j AND j)','false').replace('(j AND !j)','true').replace('(!j AND !j)','true').replace('!(j AND !j)','true').replace('!(!j AND !j)','true').replace('!(j AND !j)','true').replace('!(!j AND !j)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(k AND !k)','false').replace('(k AND a)','true').replace('(k AND b)','true').replace('(k AND c)','true').replace('(k AND d)','true').replace('(k AND e)','true').replace('(k AND f)','true').replace('(k AND g)','true').replace('(k AND i)','true').replace('(k AND h)','true').replace('(k AND j)','true').replace('(k AND k)','true').replace('(k AND l)','true').replace('(k AND m)','true').replace('(k AND n)','true').replace('(k AND o)','true').replace('(k AND p)','true').replace('(k AND q)','true').replace('(k AND r)','true').replace('(k AND s)','true').replace('(k AND t)','true').replace('(k AND u)','true').replace('(k AND v)','true').replace('(k AND w)','true').replace('(k AND x)','true').replace('(k AND y)','true').replace('(k AND z)','true').replace('(!k AND k)','false').replace('(k AND !k)','true').replace('(!k AND !k)','true').replace('!(k AND !k)','true').replace('!(!k AND !k)','true').replace('!(k AND !k)','true').replace('!(!k AND !k)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(l AND !l)','false').replace('(l AND a)','true').replace('(l AND b)','true').replace('(l AND c)','true').replace('(l AND d)','true').replace('(l AND e)','true').replace('(l AND f)','true').replace('(l AND g)','true').replace('(l AND i)','true').replace('(l AND h)','true').replace('(l AND j)','true').replace('(l AND k)','true').replace('(l AND l)','true').replace('(l AND m)','true').replace('(l AND n)','true').replace('(l AND o)','true').replace('(l AND p)','true').replace('(l AND q)','true').replace('(l AND r)','true').replace('(l AND s)','true').replace('(l AND t)','true').replace('(l AND u)','true').replace('(l AND v)','true').replace('(l AND w)','true').replace('(l AND x)','true').replace('(l AND y)','true').replace('(l AND z)','true').replace('(!l AND l)','false').replace('(l AND !l)','true').replace('(!l AND !l)','true').replace('!(l AND !l)','true').replace('!(!l AND !l)','true').replace('!(l AND !l)','true').replace('!(!l AND !l)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND 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y)','true').replace('(y AND z)','true').replace('(!y AND y)','false').replace('(y AND !y)','true').replace('(!y AND !y)','true').replace('!(y AND !y)','true').replace('!(!y AND !y)','true').replace('!(y AND !y)','true').replace('!(!y AND !y)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(z AND !z)','false').replace('(z AND a)','true').replace('(z AND b)','true').replace('(z AND c)','true').replace('(z AND d)','true').replace('(z AND e)','true').replace('(z AND f)','true').replace('(z AND g)','true').replace('(z AND i)','true').replace('(z AND h)','true').replace('(z AND j)','true').replace('(z AND k)','true').replace('(z AND l)','true').replace('(z AND m)','true').replace('(z AND n)','true').replace('(z AND o)','true').replace('(z AND p)','true').replace('(z AND q)','true').replace('(z AND r)','true').replace('(z AND s)','true').replace('(z AND t)','true').replace('(z AND u)','true').replace('(z AND v)','true').replace('(z AND w)','true').replace('(z AND x)','true').replace('(z AND y)','true').replace('(z AND z)','true').replace('(!z AND z)','false').replace('(z AND !z)','true').replace('(!z AND !z)','true').replace('!(z AND !z)','true').replace('!(!z AND !z)','true').replace('!(z AND !z)','true').replace('!(!z AND !z)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false'); } if(booleanExpression === "true"){document.write('true');} else if(booleanExpression === "false"){document.write('false');} else{document.write("true");} ​There is over 1000 different possible replacements and it definitely in constant time as described by https://en.wikipedia.org/wiki/Time_complexity I have only used nand gates though but that should be okay since all boolean circuits can be represented with nand gates. You have to use replace for it to work properly on a deterministic turing machine where each replacement is a value in the state configuration table. We can actually limit the above to just and still have the answer work out correct. booleanExpression = booleanExpression.replace('(a AND !a)','false').replace('(a AND a)','true').replace('(a AND b)','true').replace('(!a AND a)','false').replace('(a AND !a)','true').replace('(!a AND !a)','true').replace('!(a AND !a)','true').replace('!(!a AND !a)','true').replace('!(a AND !a)','true').replace('!(!a AND !a)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false').replace('(b AND !b)','false').replace('(b AND a)','true').replace('(b AND b)','true').replace('(!b AND b)','false').replace('(b AND !b)','true').replace('(!b AND !b)','true').replace('!(b AND !b)','true').replace('!(!b AND !b)','true').replace('!(b AND !b)','true').replace('!(!b AND !b)','true').replace('!(true AND !true)','false').replace('!(!false AND !true)','false').replace('!(false AND !false)','true').replace('!(!false AND !false)','false').replace('!(true AND true)','false').replace('!(false AND false)','true').replace('(true AND !true)','false').replace('(true AND false)','false').replace('(true AND !false)','true').replace('(!false AND !true)','true').replace('(false AND !false)','false').replace('(!false AND !false)','true').replace('(true AND true)','true').replace('(false AND false)','false') Since it is a heuristic it will sometimes get things wrong. It is possible to work out if it could be wrong. In which case you either have to test or improve the heuristic with more replacements. for(var i = 0; i < 4; i = i +1){ booleanExpression = booleanExpression.replace('(a AND !a)','false'); booleanExpression = booleanExpression.replace('(!a AND a)','false'); booleanExpression = booleanExpression.replace('!(a AND !a)','true'); booleanExpression = booleanExpression.replace('!(!a AND a)','true'); booleanExpression = booleanExpression.replace('(b AND !b)','false'); booleanExpression = booleanExpression.replace('(!b AND b)','false'); booleanExpression = booleanExpression.replace('!(b AND !b)','true'); booleanExpression = booleanExpression.replace('!(!b AND b)','true'); booleanExpression = booleanExpression.replace('(c AND !c)','false'); booleanExpression = booleanExpression.replace('(!c AND c)','false'); booleanExpression = booleanExpression.replace('!(c AND !c)','true'); booleanExpression = booleanExpression.replace('!(!c AND c)','true'); booleanExpression = booleanExpression.replace('(d AND !d)','false'); booleanExpression = booleanExpression.replace('(!d AND d)','false'); booleanExpression = booleanExpression.replace('!(d AND !d)','true'); booleanExpression = booleanExpression.replace('!(!d AND d)','true'); booleanExpression = booleanExpression.replace('(e AND !e)','false'); booleanExpression = booleanExpression.replace('(!e AND e)','false'); booleanExpression = booleanExpression.replace('!(e AND !e)','true'); booleanExpression = booleanExpression.replace('!(!e AND e)','true'); booleanExpression = booleanExpression.replace('(f AND !f)','false'); booleanExpression = booleanExpression.replace('(!f AND f)','false'); booleanExpression = booleanExpression.replace('!(f AND !f)','true'); booleanExpression = booleanExpression.replace('!(!f AND f)','true'); booleanExpression = booleanExpression.replace('(g AND !g)','false'); booleanExpression = booleanExpression.replace('(!g AND g)','false'); booleanExpression = booleanExpression.replace('!(g AND !g)','true'); booleanExpression = booleanExpression.replace('!(!g AND g)','true'); booleanExpression = booleanExpression.replace('(h AND !h)','false'); booleanExpression = booleanExpression.replace('(!h AND h)','false'); booleanExpression = booleanExpression.replace('!(h AND !h)','true'); booleanExpression = booleanExpression.replace('!(!h AND h)','true'); booleanExpression = booleanExpression.replace('(i AND !i)','false'); booleanExpression = booleanExpression.replace('(!i AND i)','false'); booleanExpression = booleanExpression.replace('!(i AND !i)','true'); booleanExpression = booleanExpression.replace('!(!i AND i)','true'); booleanExpression = booleanExpression.replace('(j AND !j)','false'); booleanExpression = booleanExpression.replace('(!j AND j)','false'); booleanExpression = booleanExpression.replace('!(j AND !j)','true'); booleanExpression = booleanExpression.replace('!(!j AND j)','true'); booleanExpression = booleanExpression.replace('(k AND !k)','false'); booleanExpression = booleanExpression.replace('(!k AND k)','false'); booleanExpression = booleanExpression.replace('!(k AND !k)','true'); booleanExpression = booleanExpression.replace('!(!k AND k)','true'); booleanExpression = booleanExpression.replace('(l AND !l)','false'); booleanExpression = booleanExpression.replace('(!l AND l)','false'); booleanExpression = booleanExpression.replace('!(l AND !l)','true'); booleanExpression = booleanExpression.replace('!(!l AND l)','true'); booleanExpression = booleanExpression.replace('(m AND !m)','false'); booleanExpression = booleanExpression.replace('(!m AND m)','false'); booleanExpression = booleanExpression.replace('!(m AND !m)','true'); booleanExpression = booleanExpression.replace('!(!m AND m)','true'); booleanExpression = booleanExpression.replace('(n AND !n)','false'); booleanExpression = booleanExpression.replace('(!n AND n)','false'); booleanExpression = booleanExpression.replace('!(n AND !n)','true'); booleanExpression = booleanExpression.replace('!(!n AND n)','true'); booleanExpression = booleanExpression.replace('(o AND !o)','false'); booleanExpression = booleanExpression.replace('(!o AND o)','false'); booleanExpression = booleanExpression.replace('!(o AND !o)','true'); booleanExpression = booleanExpression.replace('!(!o AND o)','true'); booleanExpression = booleanExpression.replace('(p AND !p)','false'); booleanExpression = booleanExpression.replace('(!p AND p)','false'); booleanExpression = booleanExpression.replace('!(p AND !p)','true'); booleanExpression = booleanExpression.replace('!(!p AND p)','true'); booleanExpression = booleanExpression.replace('(q AND !q)','false'); booleanExpression = booleanExpression.replace('(!q AND q)','false'); booleanExpression = booleanExpression.replace('!(q AND !q)','true'); booleanExpression = booleanExpression.replace('!(!q AND q)','true'); booleanExpression = booleanExpression.replace('(r AND !r)','false'); booleanExpression = booleanExpression.replace('(!r AND r)','false'); booleanExpression = booleanExpression.replace('!(r AND !r)','true'); booleanExpression = booleanExpression.replace('!(!r AND r)','true'); booleanExpression = booleanExpression.replace('(s AND !s)','false'); booleanExpression = booleanExpression.replace('(!s AND s)','false'); booleanExpression = booleanExpression.replace('!(s AND !s)','true'); booleanExpression = booleanExpression.replace('!(!s AND s)','true'); booleanExpression = booleanExpression.replace('(t AND !t)','false'); booleanExpression = booleanExpression.replace('(!t AND t)','false'); booleanExpression = booleanExpression.replace('!(t AND !t)','true'); booleanExpression = booleanExpression.replace('!(!t AND t)','true'); booleanExpression = booleanExpression.replace('(u AND !u)','false'); booleanExpression = booleanExpression.replace('(!u AND u)','false'); booleanExpression = booleanExpression.replace('!(u AND !u)','true'); booleanExpression = booleanExpression.replace('!(!u AND u)','true'); booleanExpression = booleanExpression.replace('(v AND !v)','false'); booleanExpression = booleanExpression.replace('(!v AND v)','false'); booleanExpression = booleanExpression.replace('!(v AND !v)','true'); booleanExpression = booleanExpression.replace('!(!v AND v)','true'); booleanExpression = booleanExpression.replace('(w AND !w)','false'); booleanExpression = booleanExpression.replace('(!w AND w)','false'); booleanExpression = booleanExpression.replace('!(w AND !w)','true'); booleanExpression = booleanExpression.replace('!(!w AND w)','true'); booleanExpression = booleanExpression.replace('(x AND !x)','false'); booleanExpression = booleanExpression.replace('(!x AND x)','false'); booleanExpression = booleanExpression.replace('!(x AND !x)','true'); booleanExpression = booleanExpression.replace('!(!x AND x)','true'); booleanExpression = booleanExpression.replace('(y AND !y)','false'); booleanExpression = booleanExpression.replace('(!y AND y)','false'); booleanExpression = booleanExpression.replace('!(y AND !y)','true'); booleanExpression = booleanExpression.replace('!(!y AND y)','true'); booleanExpression = booleanExpression.replace('(x AND !x)','false'); booleanExpression = booleanExpression.replace('(!x AND x)','false'); booleanExpression = booleanExpression.replace('!(x AND !x)','true'); booleanExpression = booleanExpression.replace('!(!x AND x)','true'); booleanExpression = booleanExpression.replace('!(true AND !true)','false'); booleanExpression = booleanExpression.replace('!(!false AND !true)','false'); booleanExpression = booleanExpression.replace('!(false AND !false)','true'); booleanExpression = booleanExpression.replace('!(!false AND !false)','false'); booleanExpression = booleanExpression.replace('!(true AND true)','false'); booleanExpression = booleanExpression.replace('!(false AND false)','true'); booleanExpression = booleanExpression.replace('(true AND !true)','false'); booleanExpression = booleanExpression.replace('(true AND false)','false'); booleanExpression = booleanExpression.replace('(true AND !false)','true'); booleanExpression = booleanExpression.replace('(!false AND !true)','true'); booleanExpression = booleanExpression.replace('(false AND !false)','false'); booleanExpression = booleanExpression.replace('(!false AND !false)','true'); booleanExpression = booleanExpression.replace('(true AND true)','true'); booleanExpression = booleanExpression.replace('(false AND false)','false'); } if(booleanExpression === "true"){document.write('true');} else if(booleanExpression === "false"){document.write('false');} else{ if(booleanExpression.length<originalbooleanExpression.length){ document.write("test"); } else { document.write("true"); } } document.write(booleanExpression);

I have improved the heuristic to run in O(1) time Basically it required a big demultiplexer that we can't really make because it is too dificult but we can make a computer generate the demultiplexer for us. package x; import java.io.BufferedReader; import java.io.File; import java.io.FileNotFoundException; import java.io.FileReader; import java.io.IOException; import java.io.PrintWriter; import java.io.UnsupportedEncodingException; import javax.script.ScriptEngine; import javax.script.ScriptEngineManager; import javax.script.ScriptException; public class Sat { public static String ORINGINAL_BOOLEAN_EXPRESSION = "((A AND NOT A) AND (A))", FILE_LOCATION = "C:/SAT/"+ORINGINAL_BOOLEAN_EXPRESSION+".txt", FILE_ENCODING = "UTF-8", SCRIPTING_ENGINE = "Javascript"; /* * write the file * */ public static void writeFile(String Result){ try{ PrintWriter writer = new PrintWriter(FILE_LOCATION, FILE_ENCODING); writer.println(Result); writer.close(); System.exit(0); } catch (IOException e) { // do something } } /* * parse out anything that isn't a letter * */ public static char[] getUniqueLetters(String expression){ String letters = expression.replaceAll("(.)\\1{1,}", "$1").replace('|', ' ').replace('!',' ').replace('&',' ').replace('(',' ').replace(')',' ').replace('=',' ').replace(" ","").replace("'",""); char[] letterarray = new char[letters.length()]; for(int i = 0; i < letters.length(); i=i+1){ letterarray[i]=letters.charAt(i); } return letterarray; }; public static int[] generateIntArray(int length){ int[] intArray = new int[length]; for(int i = 0; i < length; i=i+1){ intArray[i]=0; } return intArray; } public static String parse(String booleanExpression){ while(booleanExpression.indexOf("NAND")!=-1){ int countright = 0; int countleft = 0; int i = booleanExpression.indexOf("NAND"); while(i > -1){ if(booleanExpression.charAt(i)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(i)=='('){countright = countright+1;} if(countright > countleft){break;} i = i - 1; } booleanExpression = booleanExpression.replace(booleanExpression.substring(i, booleanExpression.indexOf("NAND")), "!"+booleanExpression.substring(i, booleanExpression.indexOf("NAND"))); booleanExpression = booleanExpression.replaceFirst("NAND", "AND"); } while(booleanExpression.indexOf("NOR")!=-1){ int countright = 0; int countleft = 0; int i = booleanExpression.indexOf("NOR"); while(i > -1){ if(booleanExpression.charAt(i)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(i)=='('){countright = countright+1;} if(countright > countleft){break;} i = i - 1; } booleanExpression = booleanExpression.replace(booleanExpression.substring(i, booleanExpression.indexOf("NOR")), "!"+booleanExpression.substring(i, booleanExpression.indexOf("NOR"))); booleanExpression = booleanExpression.replaceFirst("NOR", "OR"); } while(booleanExpression.indexOf("XOR")!=-1){ int countright = 0; int countleft = 0; int i = booleanExpression.indexOf("XOR"); while(i > -1){ if(booleanExpression.charAt(i)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(i)=='('){countright = countright+1;} if(countright > countleft){break;} i = i - 1; } countright = 0; countleft = 0; int t = booleanExpression.indexOf("XOR"); while(t < booleanExpression.length()){ if(booleanExpression.charAt(t)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(t)=='('){countright = countright+1;} t = t + 1; if(countleft > countright){break;} } booleanExpression = "("+booleanExpression.substring(i, t) + " && (" + booleanExpression.substring(i+1, booleanExpression.indexOf("XOR")-1) + "!="+ booleanExpression.substring(booleanExpression.indexOf("XOR")+3, t) +")"; booleanExpression = booleanExpression.replaceFirst("XOR", "OR"); } while(booleanExpression.indexOf("XNOR")!=-1){ int countright = 0; int countleft = 0; int i = booleanExpression.indexOf("XNOR"); while(i > -1){ if(booleanExpression.charAt(i)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(i)=='('){countright = countright+1;} if(countright > countleft){break;} i = i - 1; } countright = 0; countleft = 0; int t = booleanExpression.indexOf("XNOR"); while(t < booleanExpression.length()){ if(booleanExpression.charAt(t)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(t)=='('){countright = countright+1;} t = t + 1; if(countleft > countright){break;} } booleanExpression = "!("+booleanExpression.substring(i, t) + " && (" + booleanExpression.substring(i+1, booleanExpression.indexOf("XNOR")-1) + "!="+ booleanExpression.substring(booleanExpression.indexOf("XNOR")+4, t) +")"; booleanExpression = booleanExpression.replaceFirst("XNOR", "OR"); } booleanExpression = booleanExpression.replace("OR", "||"); booleanExpression = booleanExpression.replace("AND", "&&"); booleanExpression = booleanExpression.replace("NOT", "!"); return booleanExpression; } public static void noDuplication(String booleanExpression,char[] letterArray){ int count = 1; for(int i = 0; i < letterArray.length; i ++){ int temp = booleanExpression.length() - booleanExpression.replace(String.valueOf(letterArray[i]),"").length(); if(temp>count){ count = temp; } } if(count == 1){ System.out.println("No Duplicates"); writeFile("True"); System.exit(0); } } public static void main(String[] args) { try { File file = new File("C:/SAT/"+ORINGINAL_BOOLEAN_EXPRESSION+".txt"); if(file.exists() && !file.isDirectory()) { FileReader fileReader = new FileReader(file); BufferedReader bufferedReader = new BufferedReader(fileReader); StringBuffer stringBuffer = new StringBuffer(); String line; while ((line = bufferedReader.readLine()) != null) { stringBuffer.append(line); stringBuffer.append("\n"); } fileReader.close(); System.out.println("Contents of file:"); System.out.println(stringBuffer.toString()); System.exit(0); } } catch (IOException e) { e.printStackTrace(); } String booleanExpression = parse(ORINGINAL_BOOLEAN_EXPRESSION); while(booleanExpression.indexOf(" ")!=-1){ booleanExpression = booleanExpression.replace(" ", " "); } String output = ""; System.out.println(booleanExpression); char[] letterArray = getUniqueLetters(booleanExpression); noDuplication(booleanExpression,letterArray); while(booleanExpression.indexOf("! ")!=-1){ booleanExpression = booleanExpression.replace("! ", "!"); } boolean match = true; while (match == true){ match=false; for(int i = 0; i < letterArray.length; i ++){ while(booleanExpression.indexOf("!("+letterArray[i]+"&&"+ "!" +letterArray[i])!=-1){ booleanExpression = booleanExpression.replace(String.valueOf(letterArray[i])+"&&"+String.valueOf(letterArray[i]),"(true"); match=true; } while(booleanExpression.indexOf("!(!"+letterArray[i]+"&&" +letterArray[i])!=-1){ booleanExpression = booleanExpression.replace(String.valueOf(letterArray[i])+"&&"+String.valueOf(letterArray[i]),"(true"); match=true; } while(booleanExpression.indexOf("("+letterArray[i]+" &&"+ " !" +letterArray[i]+")")!=-1){ booleanExpression = booleanExpression.replace("("+letterArray[i]+" &&"+ " !" +letterArray[i]+")","false"); match=true; } while(booleanExpression.indexOf("(!"+letterArray[i]+" &&"+ " " +letterArray[i]+")")!=-1){ booleanExpression = booleanExpression.replace("(!"+letterArray[i]+" &&"+ " " +letterArray[i]+")","false"); match=true; } while(booleanExpression.indexOf("(false && (" +letterArray[i]+"))")!=-1) { booleanExpression = booleanExpression.replace("(false && (" +letterArray[i]+"))","true"); match=true; } while(booleanExpression.indexOf("((" +letterArray[i]+") && false)")!=-1) { booleanExpression = booleanExpression.replace("((" +letterArray[i]+") && false)","true"); match=true; } while(booleanExpression.indexOf("(true && (" +letterArray[i]+"))")!=-1) { booleanExpression = booleanExpression.replace("(true && (" +letterArray[i]+"))","true"); match=true; } while(booleanExpression.indexOf("((" +letterArray[i]+") && true)")!=-1) { booleanExpression = booleanExpression.replace("((" +letterArray[i]+") && true)","true"); match=true; } while(booleanExpression.indexOf("!(false && (" +letterArray[i]+"))")!=-1) { booleanExpression = booleanExpression.replace("!(false && (" +letterArray[i]+"))","false"); match=true; } while(booleanExpression.indexOf("!((" +letterArray[i]+") && false)")!=-1) { booleanExpression = booleanExpression.replace("!((" +letterArray[i]+") && false)","false"); match=true; } while(booleanExpression.indexOf("!(true && (" +letterArray[i]+"))")!=-1) { booleanExpression = booleanExpression.replace("!(true && (" +letterArray[i]+"))","false"); match=true; } while(booleanExpression.indexOf("!((" +letterArray[i]+") && true)")!=-1) { booleanExpression = booleanExpression.replace("!((" +letterArray[i]+") && true)","false"); match=true; } while(booleanExpression.indexOf("!((" +letterArray[i]+") || true)")!=-1) { booleanExpression = booleanExpression.replace("!((" +letterArray[i]+") || true)","false"); match=true; } while(booleanExpression.indexOf("!(true || (" +letterArray[i]+"))")!=-1) { booleanExpression = booleanExpression.replace("!(true || (" +letterArray[i]+"))","false"); match=true; } while(booleanExpression.indexOf("!((" +letterArray[i]+") || false)")!=-1) { booleanExpression = booleanExpression.replace("!((" +letterArray[i]+") || false)","false"); match=true; } while(booleanExpression.indexOf("!(false || (" +letterArray[i]+"))")!=-1) { booleanExpression = booleanExpression.replace("!(false || (" +letterArray[i]+"))","false"); match=true; } while(booleanExpression.indexOf("((" +letterArray[i]+") || true)")!=-1) { booleanExpression = booleanExpression.replace("((" +letterArray[i]+") || true)","true"); match=true; } while(booleanExpression.indexOf("(true || (" +letterArray[i]+"))")!=-1) { booleanExpression = booleanExpression.replace("(true || (" +letterArray[i]+"))","true"); match=true; } while(booleanExpression.indexOf("!(true || true)")!=-1) { booleanExpression = booleanExpression.replace("!(true || true)","true"); match=true; } while(booleanExpression.indexOf("!(true || false)")!=-1) { booleanExpression = booleanExpression.replace("!(true || false)","true"); match=true; } while(booleanExpression.indexOf("!(false || true)")!=-1) { booleanExpression = booleanExpression.replace("!((" +letterArray[i]+") && true)","true"); match=true; } while(booleanExpression.indexOf("!(false || false)")!=-1) { booleanExpression = booleanExpression.replace("!(false || false)","false"); match=true; } while(booleanExpression.indexOf("(true || true)")!=-1) { booleanExpression = booleanExpression.replace("(true || true)","true"); match=true; } while(booleanExpression.indexOf("(true || false)")!=-1) { booleanExpression = booleanExpression.replace("(true || false)","true"); match=true; } while(booleanExpression.indexOf("(false || true)")!=-1) { booleanExpression = booleanExpression.replace("(false || true)","true"); match=true; } while(booleanExpression.indexOf("(false || false)")!=-1) { booleanExpression = booleanExpression.replace("(false || false)","false"); match=true; } if(booleanExpression.indexOf("||")!=-1){ int countright = 0; int countleft = 0; int i1 = 1; while(i1 < booleanExpression.length()){ if(booleanExpression.charAt(i1)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(i1)=='('){countright = countright+1;} if((booleanExpression.charAt(i1)=='|') && (countright == countleft)){ noDuplication(booleanExpression.substring(0, i1),letterArray); noDuplication(booleanExpression.substring(i1, booleanExpression.length()).substring(0, i1),letterArray); break; } i1 = i1 + 1; } } } } System.out.println(booleanExpression); if(booleanExpression.equals("true")){ writeFile("True"); } if(booleanExpression.equals("false")){ try{ PrintWriter writer = new PrintWriter(FILE_LOCATION, FILE_ENCODING); writer.println("False"); writer.close(); } catch (IOException e) { // do something } System.exit(0); } if((booleanExpression.length() - booleanExpression.replace(String.valueOf("||"),"").length() / 2) == letterArray.length){writeFile("True");}; System.out.println("loop"); String letters = ""; for(int i = 0; i < letterArray.length; i++){ if(booleanExpression.indexOf(letterArray[i])!=-1){ letters = letters + letterArray[i]; } } char[] lettersArray2= new char[letters.length()]; if(letters.length()>0){ lettersArray2 = new char[letters.length()]; for(int i = 0; i < letters.length(); i++){ lettersArray2[i] = letters.charAt(i); } } else { PrintWriter writer; try { writer = new PrintWriter(FILE_LOCATION, FILE_ENCODING); writer.println(Boolean.parseBoolean(booleanExpression)); writer.close(); } catch (FileNotFoundException e) { // TODO Auto-generated catch block e.printStackTrace(); } catch (UnsupportedEncodingException e) { // TODO Auto-generated catch block e.printStackTrace(); } System.exit(0); } int[] intArray = generateIntArray(lettersArray2.length); while(intArray[intArray.length-1]<2){ for(int i = 0; i < intArray.length-1; i=i+1){ if(intArray[i]>1){intArray[i+1] = intArray[i+1] + 1;intArray[i]=0;} } try { ScriptEngineManager sem = new ScriptEngineManager(); ScriptEngine se = sem.getEngineByName("Javascript"); String myExpression = booleanExpression; for(int i = 0; i < intArray.length; i=i+1){ myExpression = myExpression.replace(String.valueOf(lettersArray2[i]), String.valueOf(Integer.toString(intArray[i]).charAt(0))); } System.out.println(myExpression); if(se.eval(myExpression).equals(true)){ System.out.println(myExpression); writeFile("True"); } } catch (ScriptException e1) { System.out.println("Invalid Expression"); e1.printStackTrace(); } intArray[0]=intArray[0]+1; } System.out.println(output); try{ PrintWriter writer = new PrintWriter(FILE_LOCATION, FILE_ENCODING); writer.println("False"); writer.close(); } catch (IOException e) { // do something } } }

Hey, I wrote an Artificial Intelligence program to solve SAT in polynomial time. It has a worst case runtime of O(2^N) and a best case runtime of O(1) for the first run of the program and an O(1) runtime thereafter. import java.io.BufferedReader; import java.io.File; import java.io.FileReader; import java.io.IOException; import java.io.PrintWriter; import javax.script.ScriptEngine; import javax.script.ScriptEngineManager; import javax.script.ScriptException; public class Sat { public static char[] getUniqueLetters(String expression){ String letters = expression.replaceAll("(.)\\1{1,}", "$1").replace('|', ' ').replace('!',' ').replace('&',' ').replace('(',' ').replace(')',' ').replace('=',' ').replace(" ","").replace("'",""); char[] letterarray = new char[letters.length()]; for(int i = 0; i < letters.length(); i=i+1){ letterarray[i]=letters.charAt(i); } return letterarray; }; public static int[] generateIntArray(int length){ int[] intArray = new int[length]; for(int i = 0; i < length; i=i+1){ intArray[i]=0; } return intArray; } public static String parse(String booleanExpression){ while(booleanExpression.indexOf("NAND")!=-1){ int countright = 0; int countleft = 0; int i = booleanExpression.indexOf("NAND"); while(i > -1){ if(booleanExpression.charAt(i)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(i)=='('){countright = countright+1;} if(countright > countleft){break;} i = i - 1; } booleanExpression = booleanExpression.replace(booleanExpression.substring(i, booleanExpression.indexOf("NAND")), "!"+booleanExpression.substring(i, booleanExpression.indexOf("NAND"))); booleanExpression = booleanExpression.replaceFirst("NAND", "AND"); } while(booleanExpression.indexOf("NOR")!=-1){ int countright = 0; int countleft = 0; int i = booleanExpression.indexOf("NOR"); while(i > -1){ if(booleanExpression.charAt(i)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(i)=='('){countright = countright+1;} if(countright > countleft){break;} i = i - 1; } booleanExpression = booleanExpression.replace(booleanExpression.substring(i, booleanExpression.indexOf("NOR")), "!"+booleanExpression.substring(i, booleanExpression.indexOf("NOR"))); booleanExpression = booleanExpression.replaceFirst("NOR", "OR"); } while(booleanExpression.indexOf("XOR")!=-1){ int countright = 0; int countleft = 0; int i = booleanExpression.indexOf("XOR"); while(i > -1){ if(booleanExpression.charAt(i)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(i)=='('){countright = countright+1;} if(countright > countleft){break;} i = i - 1; } countright = 0; countleft = 0; int t = booleanExpression.indexOf("XOR"); while(t < booleanExpression.length()){ if(booleanExpression.charAt(t)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(t)=='('){countright = countright+1;} t = t + 1; if(countleft > countright){break;} } booleanExpression = "("+booleanExpression.substring(i, t) + " && (" + booleanExpression.substring(i+1, booleanExpression.indexOf("XOR")-1) + "!="+ booleanExpression.substring(booleanExpression.indexOf("XOR")+3, t) +")"; booleanExpression = booleanExpression.replaceFirst("XOR", "OR"); } while(booleanExpression.indexOf("XNOR")!=-1){ int countright = 0; int countleft = 0; int i = booleanExpression.indexOf("XNOR"); while(i > -1){ if(booleanExpression.charAt(i)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(i)=='('){countright = countright+1;} if(countright > countleft){break;} i = i - 1; } countright = 0; countleft = 0; int t = booleanExpression.indexOf("XNOR"); while(t < booleanExpression.length()){ if(booleanExpression.charAt(t)==')'){countleft = countleft + 1;} if(booleanExpression.charAt(t)=='('){countright = countright+1;} t = t + 1; if(countleft > countright){break;} } booleanExpression = "!("+booleanExpression.substring(i, t) + " && (" + booleanExpression.substring(i+1, booleanExpression.indexOf("XNOR")-1) + "!="+ booleanExpression.substring(booleanExpression.indexOf("XNOR")+4, t) +")"; booleanExpression = booleanExpression.replaceFirst("XNOR", "OR"); } booleanExpression = booleanExpression.replace("OR", "||"); booleanExpression = booleanExpression.replace("AND", "&&"); booleanExpression = booleanExpression.replace("NOT", "!"); return booleanExpression; } public static void main(String[] args) { String origbooleanExpression = "(A NAND ((((A === B) AND (A === C)) NAND (NOT(A) === C)) AND (NOT(A))))"; try { File file = new File("C:/SAT/"+origbooleanExpression+".txt"); if(file.exists() && !file.isDirectory()) { FileReader fileReader = new FileReader(file); BufferedReader bufferedReader = new BufferedReader(fileReader); StringBuffer stringBuffer = new StringBuffer(); String line; while ((line = bufferedReader.readLine()) != null) { stringBuffer.append(line); stringBuffer.append("\n"); } fileReader.close(); System.out.println("Contents of file:"); System.out.println(stringBuffer.toString()); System.exit(0); } } catch (IOException e) { e.printStackTrace(); } String booleanExpression = parse(origbooleanExpression); String output = ""; System.out.println(booleanExpression); char[] letterArray = getUniqueLetters(booleanExpression); int[] intArray = generateIntArray(letterArray.length); while(intArray[intArray.length-1]<2){ for(int i = 0; i < intArray.length-1; i=i+1){ if(intArray[i]>1){intArray[i+1] = intArray[i+1] + 1;intArray[i]=0;} } try { ScriptEngineManager sem = new ScriptEngineManager(); ScriptEngine se = sem.getEngineByName("JavaScript"); String myExpression = booleanExpression; for(int i = 0; i < intArray.length; i=i+1){ myExpression = myExpression.replace(String.valueOf(letterArray[i]), String.valueOf(Integer.toString(intArray[i]).charAt(0))); } if(se.eval(myExpression).equals(true)){ System.out.println(myExpression); try{ PrintWriter writer = new PrintWriter("C:/SAT/"+origbooleanExpression+".txt", "UTF-8"); writer.println("True"); writer.close(); } catch (IOException e) { // do something } System.exit(0); } } catch (ScriptException e1) { System.out.println("Invalid Expression"); e1.printStackTrace(); } intArray[0]=intArray[0]+1; } System.out.println(output); try{ PrintWriter writer = new PrintWriter("C:/SAT/"+origbooleanExpression+".txt", "UTF-8"); writer.println("False"); writer.close(); } catch (IOException e) { // do something } } }

Hey, I think I'm basically done I dunno what more to add to it?? I wound up splitting the problem into two parts because there are two possible ways to interpret the question because the definition of nondeterminism changed. P=NP and P! = NP.pdf

So does wikipedia https://en.wikipedia.org/wiki/Nuclear_transmutation They gave the following equation. 197Au + n → 198Au (half-life 2.7 days) → 198Hg + n → 199Hg + n → 200Hg + n → 201Hg + n → 202Hg + n → 203Hg (halflife 47 days) → 203Tl + n → 204Tl (halflife 3.8 years) → 204Pb

It is possible to make gold it is just ridiculously expensive to do so. You're talking about a million times the current price of gold.

You could use GTK+ for example. #include <gtk/gtk.h> /* This is a callback function. The data arguments are ignored * in this example. More on callbacks below. */ static void hello( GtkWidget *widget, gpointer data ) { g_print ("My first GUI\n"); } static gboolean delete_event( GtkWidget *widget, GdkEvent *event, gpointer data ) { /* If you return FALSE in the "delete-event" signal handler, * GTK will emit the "destroy" signal. Returning TRUE means * you don't want the window to be destroyed. * This is useful for popping up 'are you sure you want to quit?' * type dialogs. */ g_print ("delete event occurred\n"); /* Change TRUE to FALSE and the main window will be destroyed with * a "delete-event". */ return TRUE; } /* Another callback */ static void destroy( GtkWidget *widget, gpointer data ) { gtk_main_quit (); } int main( int argc, char *argv[] ) { /* GtkWidget is the storage type for widgets */ GtkWidget *window; GtkWidget *button; /* This is called in all GTK applications. Arguments are parsed * from the command line and are returned to the application. */ gtk_init (&argc, &argv); /* create a new window */ window = gtk_window_new (GTK_WINDOW_TOPLEVEL); /* When the window is given the "delete-event" signal (this is given * by the window manager, usually by the "close" option, or on the * titlebar), we ask it to call the delete_event () function * as defined above. The data passed to the callback * function is NULL and is ignored in the callback function. */ g_signal_connect (window, "delete-event", G_CALLBACK (delete_event), NULL); /* Here we connect the "destroy" event to a signal handler. * This event occurs when we call gtk_widget_destroy() on the window, * or if we return FALSE in the "delete-event" callback. */ g_signal_connect (window, "destroy", G_CALLBACK (destroy), NULL); /* Sets the border width of the window. */ gtk_container_set_border_width (GTK_CONTAINER (window), 10); /* Creates a new button with the label "Hello World". */ button = gtk_button_new_with_label ("Hello World"); /* When the button receives the "clicked" signal, it will call the * function hello() passing it NULL as its argument. The hello() * function is defined above. */ g_signal_connect (button, "clicked", G_CALLBACK (hello), NULL); /* This will cause the window to be destroyed by calling * gtk_widget_destroy(window) when "clicked". Again, the destroy * signal could come from here, or the window manager. */ g_signal_connect_swapped (button, "clicked", G_CALLBACK (gtk_widget_destroy), window); /* This packs the button into the window (a gtk container). */ gtk_container_add (GTK_CONTAINER (window), button); /* The final step is to display this newly created widget. */ gtk_widget_show (button); /* and the window */ gtk_widget_show (window); /* All GTK applications must have a gtk_main(). Control ends here * and waits for an event to occur (like a key press or * mouse event). */ gtk_main (); return 0; } You will need to write a program to get the .json to work correctly though since it doesn't seem to use `pkg-config` properly.

They won't replace doctors, nurses, teachers or hospitality workers either. Most people like to be able to talk to a person not a robot.

Yeah pretty sure. Maybe a reduction in the workload of some sectors for instance self-cleaning appliances for chefs means they won't have to work as long.

Much the same as today.

That's a very broad question. On windows, linux or mac?

They get paid here over the summer. That's what they say but really you won't have tests every week and most schools here have 30 children and it takes like 10 seconds to grade each test.

Primary school teaching is about 6 hours a day then you have christmas and summer off.

I have put together a second draft of the paper I am writing. P vs NP (second draft).pdf