Prove that the language L = {< M > | M when started on the blank...
Prove that the language L = {< M > | M when started on the blank tape, eventually writes a $ somewhere on the tape} is undecidable.
Use the undecidability of ATM to do this. Does it matter what symbol we choose for this? What about a 1?
Homework Answers
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 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.
(3) Prove that the following language is undecidable L {< M, w> M accepts exactly three...
(3) Prove that the following language is undecidable L {< M, w> M accepts exactly three strings }. Use a reduction from ArM
Problem 2. (Undecidable) and prove it (33 points) Formulate the following problem as a language is...
Problem 2. (Undecidable) and prove it (33 points) Formulate the following problem as a language is undecidable Given a Turing machine M determine whether L(M) is context-free Hint: you can reduce the ATM problem to this problem, as we did for the REGULARTM language problem that we discussed in class.
3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10n + 4 steps th...
3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10n + 4 steps the machine will be in state 3 with the tape reading: ..00111)011100 That is, although there are three states with halting instructions, show why none of those instructions is actually encountered, and formulate this into a proof that this machine does not halt when started with a blank tape
3. Use Mathematical Induction on n to...
0 1ORO 1RI 2 1R41R5 3 OR11L3 3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank...
0 1ORO 1RI 2 1R41R5 3 OR11L3 3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10n 4 steps the machine wil be in state 3 with the tape reading:001)"011100... That is, although there are three states with halting instructions, show why none of those instructions is actually encountered, and formulate this into a proof that this machine does not halt when started with a blank tape.
0 1ORO...
3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10 n + 4 steps the machine will be in state 3 with the tape reading: ...0(0111)"011100.... T...
3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10 n + 4 steps the machine will be in state 3 with the tape reading: ...0(0111)"011100.... That is, although there are three states with halting instructions, show why none of those instructions is actually encountered, and formulate this into a proof that this machine does not halt when started with a blank tape.
3. Use Mathematical Induction on n...
1L3 1L5 3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10n +4 steps the machine will be in state 3 with the tape reading: 0(0111)"011100......
1L3 1L5 3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10n +4 steps the machine will be in state 3 with the tape reading: 0(0111)"011100... That is, although there are three states with halting instructions, show why none of those instructions is actually encountered, and formulate this into a proof that this machine does not halt when started with a blank tape.
1L3 1L5 3. Use Mathematical Induction...
2. Prove that {a"6"c" |m,n0}is not a regular language. Answer: 3. Let L = { M...
2. Prove that {a"6"c" |m,n0}is not a regular language. Answer: 3. Let L = { M M is a Turing machine and L(M) is empty), where L(M) is the language accepted by M. Prove L is undecidable by finding a reduction from Aty to it, where Arm {<M.w>M is a Turing machine and M accepts Answer: 4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then a polynomial time algorithm...
Help me answer this question plz! 4. Let L = { (A) M is a Turing...
Help me answer this question plz!
4. Let L = { (A) M is a Turing machine that accepts more than one string } a) Define the notions of Turing-recognisable language and undecidable language. b) Is L Turing-recognisable? Justify your answer with an informal argument. c) Justify with a formal proof your answer to b) d) Prove that L is undecidable. (Hint: use Rice's theorem.) e) Modify your answer to b) when instead of L you have the language Ln...
roblem 18 [15 points Consider the Turing M (Q,E, T,6,4, F), such that 16 g transition set (d) Write a regular expresion that defitves L. fsuch a regular expression does mot exist, prove it Answer...
roblem 18 [15 points Consider the Turing M (Q,E, T,6,4, F), such that 16 g transition set (d) Write a regular expresion that defitves L. fsuch a regular expression does mot exist, prove it Answer: E, N,t,1, R (M has an one-way infinite tape (infinite to the right only.) B is the designated blank symbol. M accepts by final state.) Let L be the set of strings which M accepts Let LR be the set of strings which M rejects....
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.
(3) Prove that the following language is undecidable L {< M, w> M accepts exactly three strings }. Use a reduction from ArM
Problem 2. (Undecidable) and prove it (33 points) Formulate the following problem as a language is undecidable Given a Turing machine M determine whether L(M) is context-free Hint: you can reduce the ATM problem to this problem, as we did for the REGULARTM language problem that we discussed in class.
3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10n + 4 steps the machine will be in state 3 with the tape reading: ..00111)011100 That is, although there are three states with halting instructions, show why none of those instructions is actually encountered, and formulate this into a proof that this machine does not halt when started with a blank tape
3. Use Mathematical Induction on n to...
0 1ORO 1RI 2 1R41R5 3 OR11L3 3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10n 4 steps the machine wil be in state 3 with the tape reading:001)"011100... That is, although there are three states with halting instructions, show why none of those instructions is actually encountered, and formulate this into a proof that this machine does not halt when started with a blank tape.
0 1ORO...
3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10 n + 4 steps the machine will be in state 3 with the tape reading: ...0(0111)"011100.... That is, although there are three states with halting instructions, show why none of those instructions is actually encountered, and formulate this into a proof that this machine does not halt when started with a blank tape.
3. Use Mathematical Induction on n...
1L3 1L5 3. Use Mathematical Induction on n to prove that if the TM (above) is started with a blank tape, after 10n +4 steps the machine will be in state 3 with the tape reading: 0(0111)"011100... That is, although there are three states with halting instructions, show why none of those instructions is actually encountered, and formulate this into a proof that this machine does not halt when started with a blank tape.
1L3 1L5 3. Use Mathematical Induction...
2. Prove that {a"6"c" |m,n0}is not a regular language. Answer: 3. Let L = { M M is a Turing machine and L(M) is empty), where L(M) is the language accepted by M. Prove L is undecidable by finding a reduction from Aty to it, where Arm {<M.w>M is a Turing machine and M accepts Answer: 4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then a polynomial time algorithm...
Help me answer this question plz!
4. Let L = { (A) M is a Turing machine that accepts more than one string } a) Define the notions of Turing-recognisable language and undecidable language. b) Is L Turing-recognisable? Justify your answer with an informal argument. c) Justify with a formal proof your answer to b) d) Prove that L is undecidable. (Hint: use Rice's theorem.) e) Modify your answer to b) when instead of L you have the language Ln...
roblem 18 [15 points Consider the Turing M (Q,E, T,6,4, F), such that 16 g transition set (d) Write a regular expresion that defitves L. fsuch a regular expression does mot exist, prove it Answer: E, N,t,1, R (M has an one-way infinite tape (infinite to the right only.) B is the designated blank symbol. M accepts by final state.) Let L be the set of strings which M accepts Let LR be the set of strings which M rejects....
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