Is a language recuresively enumerable _mathstackexchange?
Answers
Answered by
1
Define min(L)min(L), an operation over a language, as follows:
min(L)={w∣∄x∈L,y∈Σ+,w=xy}
min(L)={w∣∄x∈L,y∈Σ+,w=xy}
In words: all strings in language L that don't have a proper prefix in LL
Question: Recursively enumerable languages (RE) are closed under minmin? That is, if LL is RE, is min(L)min(L) also RE?
I think the answer is NO, because in order to accept a string ww, the Turing machine for min(L)min(L) would have to test all prefixes of ww, ensuring that none belongs to LL. However, since LL is RE, its Turing machine is not guaranteed to halt on all inputs.
Even if my explanation makes sense (does it?), it will not be accepted as a proof in my final exam. I need to show a reduction from a known non-RE language to min(L)min(L). But I don't know how
min(L)={w∣∄x∈L,y∈Σ+,w=xy}
min(L)={w∣∄x∈L,y∈Σ+,w=xy}
In words: all strings in language L that don't have a proper prefix in LL
Question: Recursively enumerable languages (RE) are closed under minmin? That is, if LL is RE, is min(L)min(L) also RE?
I think the answer is NO, because in order to accept a string ww, the Turing machine for min(L)min(L) would have to test all prefixes of ww, ensuring that none belongs to LL. However, since LL is RE, its Turing machine is not guaranteed to halt on all inputs.
Even if my explanation makes sense (does it?), it will not be accepted as a proof in my final exam. I need to show a reduction from a known non-RE language to min(L)min(L). But I don't know how
Similar questions