Does my solution show that the language is uncomputable by applying rice's theorem?
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.
So I'm trying to figure out how to solve this question and here is the answer that I've come up with:
(i) So we know that A is a non-trivial problem since some turing machines L(p) is a finite state and some turing machines where L(p) is not a finite state.
(ii) A respects equivalence when given any 2 equivalent turing machines p and q.
p ε A ⇒ p is a turing machine and L(p) is a finite set
⇒ q is a turing machine and L(q) is a finite set
⇒ q ε A
Therefore, by applying Rice's theorem we can see that A is uncomputable.
automation discrete-mathematics turing-machines computability
asked Nov 13 '18 at 23:15
ken6208ken6208
95
add a comment |
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.
So I'm trying to figure out how to solve this question and here is the answer that I've come up with:
(i) So we know that A is a non-trivial problem since some turing machines L(p) is a finite state and some turing machines where L(p) is not a finite state.
(ii) A respects equivalence when given any 2 equivalent turing machines p and q.
p ε A ⇒ p is a turing machine and L(p) is a finite set
⇒ q is a turing machine and L(q) is a finite set
⇒ q ε A
Therefore, by applying Rice's theorem we can see that A is uncomputable.
automation discrete-mathematics turing-machines computability
asked Nov 13 '18 at 23:15
ken6208ken6208
95
This looks good to me :)
– Patrick87
Nov 14 '18 at 20:38
add a comment |
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.
So I'm trying to figure out how to solve this question and here is the answer that I've come up with:
(i) So we know that A is a non-trivial problem since some turing machines L(p) is a finite state and some turing machines where L(p) is not a finite state.
(ii) A respects equivalence when given any 2 equivalent turing machines p and q.
p ε A ⇒ p is a turing machine and L(p) is a finite set
⇒ q is a turing machine and L(q) is a finite set
⇒ q ε A
Therefore, by applying Rice's theorem we can see that A is uncomputable.
automation discrete-mathematics turing-machines computability
asked Nov 13 '18 at 23:15
ken6208ken6208
95
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.
So I'm trying to figure out how to solve this question and here is the answer that I've come up with:
(i) So we know that A is a non-trivial problem since some turing machines L(p) is a finite state and some turing machines where L(p) is not a finite state.
(ii) A respects equivalence when given any 2 equivalent turing machines p and q.
p ε A ⇒ p is a turing machine and L(p) is a finite set
⇒ q is a turing machine and L(q) is a finite set
⇒ q ε A
Therefore, by applying Rice's theorem we can see that A is uncomputable.
automation discrete-mathematics turing-machines computability
automation discrete-mathematics turing-machines computability
asked Nov 13 '18 at 23:15
ken6208ken6208
95
asked Nov 13 '18 at 23:15
ken6208ken6208
95
asked Nov 13 '18 at 23:15
ken6208ken6208
95
asked Nov 13 '18 at 23:15
ken6208ken6208
95
asked Nov 13 '18 at 23:15
ken6208ken6208
95
95
This looks good to me :)
– Patrick87
Nov 14 '18 at 20:38
add a comment |
This looks good to me :)
– Patrick87
Nov 14 '18 at 20:38
This looks good to me :)
– Patrick87
Nov 14 '18 at 20:38
This looks good to me :)
– Patrick87
Nov 14 '18 at 20:38
add a comment |
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This looks good to me :)
– Patrick87
Nov 14 '18 at 20:38