Prove that NP is closed under karp reduction?Space(n) not closed under Karp reductions - what about NTime(n)?Class P is closed under rotation?Prove or disprove that $NL$ is closed under polynomial many-one reductions$mathbfNC_2$ is closed under log-space reductionOn Karp reductionwhen can I know if a class (complexity) is closed under reduction (cook/karp)Check if class $PSPACE$ is closed under polyonomially space reductionIs NPSPACE also closed under polynomial-time reduction and under log-space reduction?Prove PSPACE is closed under complement?Prove PSPACE is closed under union?
How can I make my BBEG immortal short of making them a Lich or Vampire?
What are these boxed doors outside store fronts in New York?
Why are 150k or 200k jobs considered good when there are 300k+ births a month?
Dragon forelimb placement
What defenses are there against being summoned by the Gate spell?
Mage Armor with Defense fighting style (for Adventurers League bladeslinger)
Writing rule stating superpower from different root cause is bad writing
Is a tag line useful on a cover?
Risk of getting Chronic Wasting Disease in the US?
Font hinting is lost in Chrome-like browsers (for some languages )
A newer friend of my brother's gave him a load of baseball cards that are supposedly extremely valuable. Is this a scam?
Minkowski space
TGV timetables / schedules?
How is the claim "I am in New York only if I am in America" the same as "If I am in New York, then I am in America?
What's the point of deactivating Num Lock on login screens?
Why, historically, did Gödel think CH was false?
Theorems that impeded progress
Test if tikzmark exists on same page
Finding angle with pure Geometry.
Why "Having chlorophyll without photosynthesis is actually very dangerous" and "like living with a bomb"?
Is it legal for company to use my work email to pretend I still work there?
Why is consensus so controversial in Britain?
How did the USSR manage to innovate in an environment characterized by government censorship and high bureaucracy?
How much RAM could one put in a typical 80386 setup?
Prove that NP is closed under karp reduction?
Space(n) not closed under Karp reductions - what about NTime(n)?Class P is closed under rotation?Prove or disprove that $NL$ is closed under polynomial many-one reductions$mathbfNC_2$ is closed under log-space reductionOn Karp reductionwhen can I know if a class (complexity) is closed under reduction (cook/karp)Check if class $PSPACE$ is closed under polyonomially space reductionIs NPSPACE also closed under polynomial-time reduction and under log-space reduction?Prove PSPACE is closed under complement?Prove PSPACE is closed under union?
$begingroup$
A complexity class $mathbbC$ is said to be closed under a reduction if:
$A$ reduces to $B$ and $B in mathbbC$ $implies$ $A in mathbbC$
How would you go about proving this if $mathbbC = NP$ and the reduction to be the karp reduction? i.e.
Prove that if $A$ karp reduces to $B$ and $B in NP$ $implies$ $A in NP$
complexity-theory
asked 3 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
A complexity class $mathbbC$ is said to be closed under a reduction if:
$A$ reduces to $B$ and $B in mathbbC$ $implies$ $A in mathbbC$
How would you go about proving this if $mathbbC = NP$ and the reduction to be the karp reduction? i.e.
Prove that if $A$ karp reduces to $B$ and $B in NP$ $implies$ $A in NP$
complexity-theory
asked 3 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
2
$begingroup$
Try using the definitions.
$endgroup$
– Yuval Filmus
3 hours ago
$begingroup$
@YuvalFilmus thanks for the advice, this helped me figure it out!
$endgroup$
– Ankit Bahl
2 hours ago
add a comment |
$begingroup$
A complexity class $mathbbC$ is said to be closed under a reduction if:
$A$ reduces to $B$ and $B in mathbbC$ $implies$ $A in mathbbC$
How would you go about proving this if $mathbbC = NP$ and the reduction to be the karp reduction? i.e.
Prove that if $A$ karp reduces to $B$ and $B in NP$ $implies$ $A in NP$
complexity-theory
asked 3 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
A complexity class $mathbbC$ is said to be closed under a reduction if:
$A$ reduces to $B$ and $B in mathbbC$ $implies$ $A in mathbbC$
How would you go about proving this if $mathbbC = NP$ and the reduction to be the karp reduction? i.e.
Prove that if $A$ karp reduces to $B$ and $B in NP$ $implies$ $A in NP$
complexity-theory
complexity-theory
asked 3 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
Ankit BahlAnkit Bahl
262
asked 3 hours ago
Ankit BahlAnkit Bahl
262
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
$begingroup$
Try using the definitions.
$endgroup$
– Yuval Filmus
3 hours ago
$begingroup$
@YuvalFilmus thanks for the advice, this helped me figure it out!
$endgroup$
– Ankit Bahl
2 hours ago
add a comment |
2
$begingroup$
Try using the definitions.
$endgroup$
– Yuval Filmus
3 hours ago
$begingroup$
@YuvalFilmus thanks for the advice, this helped me figure it out!
$endgroup$
– Ankit Bahl
2 hours ago
2
2
$begingroup$
Try using the definitions.
$endgroup$
– Yuval Filmus
3 hours ago
$begingroup$
Try using the definitions.
$endgroup$
– Yuval Filmus
3 hours ago
$begingroup$
@YuvalFilmus thanks for the advice, this helped me figure it out!
$endgroup$
– Ankit Bahl
2 hours ago
$begingroup$
@YuvalFilmus thanks for the advice, this helped me figure it out!
$endgroup$
– Ankit Bahl
2 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I was able to figure it out. In case anyone was wondering:
$B in NP$ means that there exists a non-deterministic polynomial time algorithm for $B$. Let's call that $b(i)$, where i is the input to $B$.
$A$ karp reducing to $B implies$ that there exists a function $m$ such that $m$ can take an input $i$ to $A$ and map it to some input $m(i)$ for $B$, and if an instance of $i$ is true for $A$ then $m(i)$ is true for B (and vice versa),
Therefore, an algorithm for $A$ can be made as follows:
$A (i)$
- Take input $i$ and apply $m$ to yield $m(i)$
- Apply $b$ with input $m(i)$
This yields an output for $A$. Since both $m$ and $b$ are non-deterministic polynomial time, this algorithm is non-deterministic polynomial time. Therefore $A$ must be in NP.
answered 2 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "419"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Ankit Bahl is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcs.stackexchange.com%2fquestions%2f106574%2fprove-that-np-is-closed-under-karp-reduction%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I was able to figure it out. In case anyone was wondering:
$B in NP$ means that there exists a non-deterministic polynomial time algorithm for $B$. Let's call that $b(i)$, where i is the input to $B$.
$A$ karp reducing to $B implies$ that there exists a function $m$ such that $m$ can take an input $i$ to $A$ and map it to some input $m(i)$ for $B$, and if an instance of $i$ is true for $A$ then $m(i)$ is true for B (and vice versa),
Therefore, an algorithm for $A$ can be made as follows:
$A (i)$
- Take input $i$ and apply $m$ to yield $m(i)$
- Apply $b$ with input $m(i)$
This yields an output for $A$. Since both $m$ and $b$ are non-deterministic polynomial time, this algorithm is non-deterministic polynomial time. Therefore $A$ must be in NP.
answered 2 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I was able to figure it out. In case anyone was wondering:
$B in NP$ means that there exists a non-deterministic polynomial time algorithm for $B$. Let's call that $b(i)$, where i is the input to $B$.
$A$ karp reducing to $B implies$ that there exists a function $m$ such that $m$ can take an input $i$ to $A$ and map it to some input $m(i)$ for $B$, and if an instance of $i$ is true for $A$ then $m(i)$ is true for B (and vice versa),
Therefore, an algorithm for $A$ can be made as follows:
$A (i)$
- Take input $i$ and apply $m$ to yield $m(i)$
- Apply $b$ with input $m(i)$
This yields an output for $A$. Since both $m$ and $b$ are non-deterministic polynomial time, this algorithm is non-deterministic polynomial time. Therefore $A$ must be in NP.
answered 2 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I was able to figure it out. In case anyone was wondering:
$B in NP$ means that there exists a non-deterministic polynomial time algorithm for $B$. Let's call that $b(i)$, where i is the input to $B$.
$A$ karp reducing to $B implies$ that there exists a function $m$ such that $m$ can take an input $i$ to $A$ and map it to some input $m(i)$ for $B$, and if an instance of $i$ is true for $A$ then $m(i)$ is true for B (and vice versa),
Therefore, an algorithm for $A$ can be made as follows:
$A (i)$
- Take input $i$ and apply $m$ to yield $m(i)$
- Apply $b$ with input $m(i)$
This yields an output for $A$. Since both $m$ and $b$ are non-deterministic polynomial time, this algorithm is non-deterministic polynomial time. Therefore $A$ must be in NP.
answered 2 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I was able to figure it out. In case anyone was wondering:
$B in NP$ means that there exists a non-deterministic polynomial time algorithm for $B$. Let's call that $b(i)$, where i is the input to $B$.
$A$ karp reducing to $B implies$ that there exists a function $m$ such that $m$ can take an input $i$ to $A$ and map it to some input $m(i)$ for $B$, and if an instance of $i$ is true for $A$ then $m(i)$ is true for B (and vice versa),
Therefore, an algorithm for $A$ can be made as follows:
$A (i)$
- Take input $i$ and apply $m$ to yield $m(i)$
- Apply $b$ with input $m(i)$
This yields an output for $A$. Since both $m$ and $b$ are non-deterministic polynomial time, this algorithm is non-deterministic polynomial time. Therefore $A$ must be in NP.
answered 2 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 hours ago
Ankit BahlAnkit Bahl
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 hours ago
Ankit BahlAnkit Bahl
262
answered 2 hours ago
Ankit BahlAnkit Bahl
262
262
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ankit Bahl is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
Ankit Bahl is a new contributor. Be nice, and check out our Code of Conduct.
Ankit Bahl is a new contributor. Be nice, and check out our Code of Conduct.
Ankit Bahl is a new contributor. Be nice, and check out our Code of Conduct.
Ankit Bahl is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Computer Science Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcs.stackexchange.com%2fquestions%2f106574%2fprove-that-np-is-closed-under-karp-reduction%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
Try using the definitions.
$endgroup$
– Yuval Filmus
3 hours ago
$begingroup$
@YuvalFilmus thanks for the advice, this helped me figure it out!
$endgroup$
– Ankit Bahl
2 hours ago