I need help with the following true or false questions:
1.The Intersection of two context-free languages is recursive.
2.For an arbitrary regular language L, the set of all strings in L that have even length forms a language that is not recursive.
3. If L is accepted by a PDA then L is accepted by a PDA that has no compatible transitions.
For clarification purposes, recursive means a that a turing machine can decide the language. Recursive enumerable means that a turing machine can recognize the language. PDA = push down automaton. Here's what i think:
1. false, since the intersection of 2 context free languages is not necessarily context free since CFLs are not closed under intersection. And if it's not CF then it can't be recursive.
2. false, not sure why tho...just my intuition
3. i wasn't sure what compatible transitions meant.
if you know the answers, that would really help me out, and also explain why. Thanks!
