0 0 votes Below is a Venn diagram showing the overlap of different classes of languages. For the language given below, tell where in the Venn diagram that language belongs.$$FIN_{TM}=\{\langle M\rangle\mid M\text{ is a TM and }L(M)\text{ is finite}\}$$ Theory of Computation goclasses goclasses-cs-dpp theory-of-computation goclasses-cs-dpp-day-391 goclasses-toc-practice-questions identify-class-language numerical-answers + – GO Classes 48 views answer comment Share Follow Print 0 reply Please log in or register to add a comment.
0 0 votes Not RE (Recursively Enumerable):A Turing machine cannot confirm that $L(M)$ is finite.To do so, it would have to check an infinite number of possible strings to guarantee that the machine eventually stops accepting new ones, which is impossible in finite time.Therefore, it is not in the RE circle. Not co-RE (co-Recursively Enumerable):A language is co-RE if its complement is RE.Here, the complement corresponds to checking whether $L(M)$ is infinite.However, a Turing machine also cannot confirm that a language is infinite. Seeing a machine accept a million strings does not prove that it will accept infinitely many strings.Therefore, it is not in the co-RE circle. Conclusion:Because $FIN_{\mathrm{TM}}$ is neither RE nor co-RE, it falls entirely outside both of those circles, placing it in Region $\mathbf{5}$. GO Classes answered 4 days ago GO Classes comment Share Follow 0 reply Please log in or register to add a comment.
