is the set {i | Dom($phi_i$) = ∅} recursive, recursive enumerable or none of them
-1
can somebody help me understand if the set {i | Dom($phi_i$) = ∅} recursive, recursive enumerable or none of them?
Dom($phi_k$) is the set {x | $phi_k$(x) ↓}.
Thank you so much
computability
asked Jan 6 at 11:04
NormanNorman
107
add a comment |
-1
can somebody help me understand if the set {i | Dom($phi_i$) = ∅} recursive, recursive enumerable or none of them?
Dom($phi_k$) is the set {x | $phi_k$(x) ↓}.
Thank you so much
computability
asked Jan 6 at 11:04
NormanNorman
107
What have you tried? What are some things you already know, or know how to do?
– Noah Schweber
Jan 6 at 11:10
What is $phi_k$ and what is $phi_k(x)$ and what is $phi_k(x)↓$?
– drhab
Jan 6 at 11:13
@drhab That is standard notation in computability theory: $phi_k$ is the $k$th partial computable function (in a fixed appropriate enumeration) and "$downarrow$" means "is defined" (or "converges" or "halts").
– Noah Schweber
Jan 6 at 11:38
@NoahSchweber Thank you for your answer. Honestly i couldn't do anything for this example. i know there are few techniques to use like Rice theorem or reduction to well known problems like Halting problem or something like that. but couldn't find my way
– Norman
Jan 6 at 12:11
@Norman Well, let's start with Rice's theorem - what does it say, and is it applicable here?
– Noah Schweber
Jan 6 at 12:11
add a comment |
-1
-1
-1
can somebody help me understand if the set {i | Dom($phi_i$) = ∅} recursive, recursive enumerable or none of them?
Dom($phi_k$) is the set {x | $phi_k$(x) ↓}.
Thank you so much
computability
asked Jan 6 at 11:04
NormanNorman
107
can somebody help me understand if the set {i | Dom($phi_i$) = ∅} recursive, recursive enumerable or none of them?
Dom($phi_k$) is the set {x | $phi_k$(x) ↓}.
Thank you so much
computability
computability
asked Jan 6 at 11:04
NormanNorman
107
asked Jan 6 at 11:04
NormanNorman
107
asked Jan 6 at 11:04
NormanNorman
107
asked Jan 6 at 11:04
NormanNorman
107
asked Jan 6 at 11:04
NormanNorman
107
107
What have you tried? What are some things you already know, or know how to do?
– Noah Schweber
Jan 6 at 11:10
What is $phi_k$ and what is $phi_k(x)$ and what is $phi_k(x)↓$?
– drhab
Jan 6 at 11:13
@drhab That is standard notation in computability theory: $phi_k$ is the $k$th partial computable function (in a fixed appropriate enumeration) and "$downarrow$" means "is defined" (or "converges" or "halts").
– Noah Schweber
Jan 6 at 11:38
@NoahSchweber Thank you for your answer. Honestly i couldn't do anything for this example. i know there are few techniques to use like Rice theorem or reduction to well known problems like Halting problem or something like that. but couldn't find my way
– Norman
Jan 6 at 12:11
@Norman Well, let's start with Rice's theorem - what does it say, and is it applicable here?
– Noah Schweber
Jan 6 at 12:11
add a comment |
What have you tried? What are some things you already know, or know how to do?
– Noah Schweber
Jan 6 at 11:10
What is $phi_k$ and what is $phi_k(x)$ and what is $phi_k(x)↓$?
– drhab
Jan 6 at 11:13
@drhab That is standard notation in computability theory: $phi_k$ is the $k$th partial computable function (in a fixed appropriate enumeration) and "$downarrow$" means "is defined" (or "converges" or "halts").
– Noah Schweber
Jan 6 at 11:38
@NoahSchweber Thank you for your answer. Honestly i couldn't do anything for this example. i know there are few techniques to use like Rice theorem or reduction to well known problems like Halting problem or something like that. but couldn't find my way
– Norman
Jan 6 at 12:11
@Norman Well, let's start with Rice's theorem - what does it say, and is it applicable here?
– Noah Schweber
Jan 6 at 12:11
What have you tried? What are some things you already know, or know how to do?
– Noah Schweber
Jan 6 at 11:10
What have you tried? What are some things you already know, or know how to do?
– Noah Schweber
Jan 6 at 11:10
What is $phi_k$ and what is $phi_k(x)$ and what is $phi_k(x)↓$?
– drhab
Jan 6 at 11:13
What is $phi_k$ and what is $phi_k(x)$ and what is $phi_k(x)↓$?
– drhab
Jan 6 at 11:13
@drhab That is standard notation in computability theory: $phi_k$ is the $k$th partial computable function (in a fixed appropriate enumeration) and "$downarrow$" means "is defined" (or "converges" or "halts").
– Noah Schweber
Jan 6 at 11:38
@drhab That is standard notation in computability theory: $phi_k$ is the $k$th partial computable function (in a fixed appropriate enumeration) and "$downarrow$" means "is defined" (or "converges" or "halts").
– Noah Schweber
Jan 6 at 11:38
@NoahSchweber Thank you for your answer. Honestly i couldn't do anything for this example. i know there are few techniques to use like Rice theorem or reduction to well known problems like Halting problem or something like that. but couldn't find my way
– Norman
Jan 6 at 12:11
@NoahSchweber Thank you for your answer. Honestly i couldn't do anything for this example. i know there are few techniques to use like Rice theorem or reduction to well known problems like Halting problem or something like that. but couldn't find my way
– Norman
Jan 6 at 12:11
@Norman Well, let's start with Rice's theorem - what does it say, and is it applicable here?
– Noah Schweber
Jan 6 at 12:11
@Norman Well, let's start with Rice's theorem - what does it say, and is it applicable here?
– Noah Schweber
Jan 6 at 12:11
add a comment |
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What have you tried? What are some things you already know, or know how to do?
– Noah Schweber
Jan 6 at 11:10
What is $phi_k$ and what is $phi_k(x)$ and what is $phi_k(x)↓$?
– drhab
Jan 6 at 11:13
@drhab That is standard notation in computability theory: $phi_k$ is the $k$th partial computable function (in a fixed appropriate enumeration) and "$downarrow$" means "is defined" (or "converges" or "halts").
– Noah Schweber
Jan 6 at 11:38
@NoahSchweber Thank you for your answer. Honestly i couldn't do anything for this example. i know there are few techniques to use like Rice theorem or reduction to well known problems like Halting problem or something like that. but couldn't find my way
– Norman
Jan 6 at 12:11
@Norman Well, let's start with Rice's theorem - what does it say, and is it applicable here?
– Noah Schweber
Jan 6 at 12:11