Show that FINITETM = {<M> : M is a TM and L(M) is finite} is undecidable.
Show that FINITETM = {<M> : M is a TM and L(M) is finite} is undecidable.
5. [10 marks] Use Rice’s Theorem if possible to show the following problems are undecidable. If it is not possible to use Rice’s Theorem, explain why not. (a) [5 marks] M1TM = {< M >| M is a TM and L(M) is finite}. (b) [5 marks] M2TM = {< M >| M is a TM and L(M) is a subset of Σ ∗}.
Let REPEATTM = { | M is a TM, and for all s L(M), s = uv where
u = v }. Show that REPEATTM is undecidable. Do not use Rice’s
Theorem.
Let REPEATTM = { <M>M is a TM, and for all s E L(M), s = uv where u = v}. Show that REPEATM is undecidable. Do not use Rice's Theorem.
(10) Let L = { <M> | M is a TM that accepts sR whenever it accepts s } . Show that L is undecidable.
8. (15) Let REPEATTM = { <M>M is a TM, and for all s € L(M), s = uv where u = v}. Show that REPEATM is undecidable. Do not use Rice's Theorem.
19. (1 point) Suppose that L is undecidable and L is recognizable. Which of the following could be false? A. I is co-Turing recognizable. B. I is not recognizable. C. I is undecidable. D. L* is not recognizable. E. None of the above. 20. (2 points) Let ETM {(M)|L(M) = 0} and EQTM = {(M1, M2)|L(Mi) = L(M2)}. We want to show that EQTM is undecidable by reducing Etm to EQTM and we do this by assuming R is a...
Let REPEATTM = {<M> Mis a TM, and for all s E L(M), s = uv where u =v}. Show that REPEATTM is undecidable. Do not use Rice's Theorem.
Use a Turing Reduction to show that the following language is undecidable. L={ | L(M) is infinite}.
8. (15)
Let REPEATTM = { <M> | M is a TM, and for all s L(M),
s = uv where u = v }. Show that REPEATTM is undecidable. Do not use
Rice’s Theorem.
7. (15) PALINDROIVIDACI vy provimo ETUS in polynomial time. 8. (15) Let REPEATTM = { <M>M is a TM, and for all s € L(M), s = uv where u =v}. Show that REPEATTM is undecidable. Do not use Rice's Theorem. ai
Let Show that L is undecidable L = {〈M) IM is a Turing Machine that accepts w whenever it accepts L = {〈M) IM is a Turing Machine that accepts w whenever it accepts
6. (10 points) Prove that the language L = {< M 1 , M 2 >: M, , M 2 are T M s and L(M-) = L(M 2)) is undecidable.
6. (10 points) Prove that the language L = {: M, , M 2 are T M s and L(M-) = L(M 2)) is undecidable.