If p is a Turing machine then L(p) = {x | p(x) = yes}. Let A...
If p is a Turing machine then L(p) = {x | p(x) = yes}.
Let A = {p | p is a Turing machine and L(p) is a finite set}.
Is A computable? Justify your answer
Homework Answers
Yes, as L(p) is a finite set and p(x) is always equal to "yes". Then the value of A is computable.
2. Let L = {hMi: M is a Turing machine that accepts at least two binary strings}. a) Define the notions of a recognisabl...
2. Let L = {hMi: M is a Turing machine that accepts at least two
binary strings}. a) Define the notions of a recognisable language
and an undecidable language. [5 marks] b) Is L Turing-recognisable?
Justify your answer with an informal argument. [5 marks] c) Prove
that L is undecidable. (Hint: use Rice’s theorem.) [20 marks] d)
Bonus: Justify with a formal proof your answer to b). [20
marks]
2. Let L-M M): M is a Turing machine that accepts...
2. Let L-M M): M is a Turing machine that accepts at least two binary strings. a) Define the notions of a recognisable...
2. Let L-M M): M is a Turing machine that accepts at least two binary strings. a) Define the notions of a recognisable language and an undecidable language. [5 marks [5 marks] b) Is L Turing-recognisable? Justify your answer with an informal argument. c) Prove that L is undecidable. (Hint: use Rice's theorem.) [20 marks] 20 marks] d) Bonus: Justify with a formal proof your answer to b).
2. Let L-M M): M is a Turing machine that accepts at...
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...
Let h(n) =1 if n codes a Turing machine M which halts when started on a...
Let h(n) =1 if n codes a Turing machine M which halts when started on a blank tape, h(n) =0 otherwise. Sketch a proof that h is not Turing computable.
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
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
please answer and I will rate! 3. Let L = {M M is a Turing machine...
please answer and I will rate!
3. Let L = {M M is a Turing machine and L(M) is empty), where L(M) is the language accepted by M. Prove Lis undecidable by finding a reduction from Arm to it, where Ayv-<<MwM is a Turing machine and M accepts w). Answer:
3. Let L= {MM is a Turing machine and L(M) is empty), where L(M) is the...
3. Let L= {MM 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 Arm to it, where Arm={<M,w>| M is a Turing machine and M accepts w}
Let F IN = {M | L(M) is finite}, and recall HP = {M#w | M...
Let F IN = {M | L(M) is finite}, and recall HP = {M#w | M halts
on w}.
(a) Prove HP¯ ≤m F IN, where HP¯ is the complement of the
halting problem. That is, show there exists a computable function f
such that M#w ∈ HP¯ iff f(M#w) ∈ F IN.
(b) Prove HP ≤m F IN. That is, show there exists a computable
function f such that M#w ∈ HP iff f(M#w) ∈ F IN.
(c) Is...
3b. Consider the language FIN = { | M is a Turing machine and L(M) is...
3b. Consider the language FIN = { | M is a Turing machine and L(M) is finite }. Prove FIN is not decidable.
(a) Give a high level description of a single-tape deterministic Turing machine that decides the language...
(a) Give a high level description of a single-tape deterministic Turing machine that decides the language L = {w#x#y | w ∈ {0, 1} ∗ , x ∈ {0, 1} ∗ , y ∈ {0, 1} ∗ , and |w| > |x| > |y|}, where the input alphabet is Σ = {0, 1}. (b) What is the running time (order notation) of your Turing machine? Justify your answer.
2. Let L = {hMi: M is a Turing machine that accepts at least two
binary strings}. a) Define the notions of a recognisable language
and an undecidable language. [5 marks] b) Is L Turing-recognisable?
Justify your answer with an informal argument. [5 marks] c) Prove
that L is undecidable. (Hint: use Rice’s theorem.) [20 marks] d)
Bonus: Justify with a formal proof your answer to b). [20
marks]
2. Let L-M M): M is a Turing machine that accepts...
2. Let L-M M): M is a Turing machine that accepts at least two binary strings. a) Define the notions of a recognisable language and an undecidable language. [5 marks [5 marks] b) Is L Turing-recognisable? Justify your answer with an informal argument. c) Prove that L is undecidable. (Hint: use Rice's theorem.) [20 marks] 20 marks] d) Bonus: Justify with a formal proof your answer to b).
2. Let L-M M): M is a Turing machine that accepts at...
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...
please answer and I will rate!
3. Let L = {M M is a Turing machine and L(M) is empty), where L(M) is the language accepted by M. Prove Lis undecidable by finding a reduction from Arm to it, where Ayv-<<MwM is a Turing machine and M accepts w). Answer:
3. Let L= {MM 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 Arm to it, where Arm={<M,w>| M is a Turing machine and M accepts w}
Let F IN = {M | L(M) is finite}, and recall HP = {M#w | M halts
on w}.
(a) Prove HP¯ ≤m F IN, where HP¯ is the complement of the
halting problem. That is, show there exists a computable function f
such that M#w ∈ HP¯ iff f(M#w) ∈ F IN.
(b) Prove HP ≤m F IN. That is, show there exists a computable
function f such that M#w ∈ HP iff f(M#w) ∈ F IN.
(c) Is...
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