So if a problem is more difficult the language it represents is smaller?












3














I'm reading the definition of polynomial time reducible:




Let $L_1, L_2$ be two language. If $L_1$ is polynomial time reducible to $L_2$ then exists $f:{0,1}^*$ s.t. $forall xin{0,1}^*$ $$xin L_1iff f(x)in L_2$$




For me this means the $L_1$ may be bigger (in cardinality) than $L_2$, but $L_2$ is more difficult since $L_1$ can be solved after reduced to $L_2$?






np-complete reductions decision-problem







share|cite|improve this question






















  • How would define the cardinality of an infinite set being larger than another infinite set (both being countable sets)?
    – dkaeae
    7 hours ago










  • You can find examples in which $L_1$ is a strict subset of $L_2$ (and vice versa).
    – Yuval Filmus
    7 hours ago
















3














I'm reading the definition of polynomial time reducible:




Let $L_1, L_2$ be two language. If $L_1$ is polynomial time reducible to $L_2$ then exists $f:{0,1}^*$ s.t. $forall xin{0,1}^*$ $$xin L_1iff f(x)in L_2$$




For me this means the $L_1$ may be bigger (in cardinality) than $L_2$, but $L_2$ is more difficult since $L_1$ can be solved after reduced to $L_2$?






np-complete reductions decision-problem







share|cite|improve this question






















  • How would define the cardinality of an infinite set being larger than another infinite set (both being countable sets)?
    – dkaeae
    7 hours ago










  • You can find examples in which $L_1$ is a strict subset of $L_2$ (and vice versa).
    – Yuval Filmus
    7 hours ago














3












3








3







I'm reading the definition of polynomial time reducible:




Let $L_1, L_2$ be two language. If $L_1$ is polynomial time reducible to $L_2$ then exists $f:{0,1}^*$ s.t. $forall xin{0,1}^*$ $$xin L_1iff f(x)in L_2$$




For me this means the $L_1$ may be bigger (in cardinality) than $L_2$, but $L_2$ is more difficult since $L_1$ can be solved after reduced to $L_2$?






np-complete reductions decision-problem







share|cite|improve this question













I'm reading the definition of polynomial time reducible:




Let $L_1, L_2$ be two language. If $L_1$ is polynomial time reducible to $L_2$ then exists $f:{0,1}^*$ s.t. $forall xin{0,1}^*$ $$xin L_1iff f(x)in L_2$$




For me this means the $L_1$ may be bigger (in cardinality) than $L_2$, but $L_2$ is more difficult since $L_1$ can be solved after reduced to $L_2$?






np-complete reductions decision-problem




np-complete reductions decision-problem






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 8 hours ago









Bit_hcAlgorithm

1408




1408












  • How would define the cardinality of an infinite set being larger than another infinite set (both being countable sets)?
    – dkaeae
    7 hours ago










  • You can find examples in which $L_1$ is a strict subset of $L_2$ (and vice versa).
    – Yuval Filmus
    7 hours ago


















  • How would define the cardinality of an infinite set being larger than another infinite set (both being countable sets)?
    – dkaeae
    7 hours ago










  • You can find examples in which $L_1$ is a strict subset of $L_2$ (and vice versa).
    – Yuval Filmus
    7 hours ago
















How would define the cardinality of an infinite set being larger than another infinite set (both being countable sets)?
– dkaeae
7 hours ago




How would define the cardinality of an infinite set being larger than another infinite set (both being countable sets)?
– dkaeae
7 hours ago












You can find examples in which $L_1$ is a strict subset of $L_2$ (and vice versa).
– Yuval Filmus
7 hours ago




You can find examples in which $L_1$ is a strict subset of $L_2$ (and vice versa).
– Yuval Filmus
7 hours ago










1 Answer
1






active

oldest

votes


















5














$L_1$ and $L_2$ are always countably infinite, and thus "equally big".



If any language is finite, then it is "constant time" recognizable.






share|cite|improve this answer





















  • I forgot this fact that they're both infinite... Thanks!
    – Bit_hcAlgorithm
    5 hours ago











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
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcs.stackexchange.com%2fquestions%2f102213%2fso-if-a-problem-is-more-difficult-the-language-it-represents-is-smaller%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









5














$L_1$ and $L_2$ are always countably infinite, and thus "equally big".



If any language is finite, then it is "constant time" recognizable.






share|cite|improve this answer





















  • I forgot this fact that they're both infinite... Thanks!
    – Bit_hcAlgorithm
    5 hours ago
















5














$L_1$ and $L_2$ are always countably infinite, and thus "equally big".



If any language is finite, then it is "constant time" recognizable.






share|cite|improve this answer





















  • I forgot this fact that they're both infinite... Thanks!
    – Bit_hcAlgorithm
    5 hours ago














5












5








5






$L_1$ and $L_2$ are always countably infinite, and thus "equally big".



If any language is finite, then it is "constant time" recognizable.






share|cite|improve this answer












$L_1$ and $L_2$ are always countably infinite, and thus "equally big".



If any language is finite, then it is "constant time" recognizable.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 7 hours ago









Pål GD

5,9621939




5,9621939












  • I forgot this fact that they're both infinite... Thanks!
    – Bit_hcAlgorithm
    5 hours ago


















  • I forgot this fact that they're both infinite... Thanks!
    – Bit_hcAlgorithm
    5 hours ago
















I forgot this fact that they're both infinite... Thanks!
– Bit_hcAlgorithm
5 hours ago




I forgot this fact that they're both infinite... Thanks!
– Bit_hcAlgorithm
5 hours ago


















draft saved

draft discarded




















































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.





Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


Please pay close attention to the following guidance:


  • 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.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcs.stackexchange.com%2fquestions%2f102213%2fso-if-a-problem-is-more-difficult-the-language-it-represents-is-smaller%23new-answer', 'question_page');
}
);

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







-

Popular posts from this blog

Morgemoulin

Image
Morgemoulin — miejscowość i gmina — Państwo   Francja Region Grand Est Departament Moza Okręg Verdun Kod INSEE 55357 Powierzchnia 6,82 km² Populacja  (1990) • liczba ludności 75 • gęstość 11 os./km² Kod pocztowy 55400 Położenie na mapie Francji Morgemoulin 49°14′N   5°35′E / 49,233333   5,583333 Portal Francja Morgemoulin – miejscowość i gmina we Francji, w regionie Grand Est, w departamencie Moza. Według danych na rok 1990 gminę zamieszkiwało 75 osób, a gęstość zaludnienia wynosiła 11 osób/km² (wśród 2335 gmin Lotaryngii Morgemoulin plasuje się na 970. miejscu pod względem liczby ludności, natomiast pod względem powierzchni na miejscu 848.). Bibliografia | Francuski urząd statystyczny ( fr. ) . p   •   d   •   e Gminy okręgu Verdun Abaucourt-Hautecourt • Aincreville • Ambly-sur-Meuse • Amel-sur-l'Étang • Ancemont • Arrancy-sur-Crusne • Aubréville • Autré
Read more

Scott Moir

Image
Scott Moir Tessa Virtue i Scott Moir w 2016 r. Reprezentacja   Kanada Data i miejsce urodzenia 2 września 1987 London Wzrost 180 cm Konkurencja Pary taneczne Partner sportowy Tessa Virtue Trener Marie-France Dubreuil, Patrice Lauzon, Romain Haguenauer Poprzednio: Marina Zujewa, Oleg Epstein, Igor Szpilband, Johnny Johns, Carol Moir, Paul MacIntosh, Suzanne Killing Klub Montreal International School of Skating Poprzednio: Arctic Edge FSC Ilderton Skating Club Lokalizacja treningowa Montreal Poprzednio: Canton Kitchener Rekordy życiowe ISU przed sezonem 2018/2019 Nota łączna 206,07 Igrzyska Olimpijskie 2018 Taniec krótki 83,67 Igrzyska Olimpijskie 2018 Taniec dowolny 122,40 Igrzyska Olimpijskie 2018 Dorobek medalowy Reprezentacja   Kanada Igrzyska olimpijskie Złoto Vancouver 2010 pary taneczne Złoto Pjongczang 2018 pary taneczne Złoto Pjongczang 2018 drużynowo Srebro S
Read more

Souastre

Image
Souastre — miejscowość i gmina — Herb Państwo   Francja Region Hauts-de-France Departament Pas-de-Calais Okręg Arras Kod INSEE 62800 Powierzchnia 7,18 km² Populacja  (1990) • liczba ludności 352 • gęstość 49 os./km² Kod pocztowy 62111 Położenie na mapie Francji Souastre 50°09′N   2°34′E / 50,150000   2,566667 Portal Francja Souastre – miejscowość i gmina we Francji, w regionie Hauts-de-France, w departamencie Pas-de-Calais. Według danych na rok 1990 gminę zamieszkiwały 352 osoby, a gęstość zaludnienia wynosiła 49 osób/km² (wśród 1549 gmin regionu Nord-Pas-de-Calais Souastre plasuje się na 887. miejscu pod względem liczby ludności, natomiast pod względem powierzchni na miejscu 507.). Bibliografia | Francuski urząd statystyczny ( fr. ) . p   •   d   •   e Gminy okręgu Arras Ablain-Saint-Nazaire Ablainzevelle Acheville Achicourt Achiet-le-Grand Achiet-le-Pe
Read more