Tighter Hard Instances for PPSZ

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00476174" target="_blank" >RIV/67985840:_____/17:00476174 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2017.85" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ICALP.2017.85</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2017.85" target="_blank" >10.4230/LIPIcs.ICALP.2017.85</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Tighter Hard Instances for PPSZ

Popis výsledku v původním jazyce

We construct uniquely satisfiable k-CNF formulas that are hard for the PPSZ algorithm, the currently best known algorithm solving k-SAT. This algorithm tries to generate a satisfying assignment by picking a random variable at a time and attempting to derive its value using some inference heuristic and otherwise assigning a random value. The weak PPSZ checks all subformulas of a given size to derive a value and the strong PPSZ runs resolution with width bounded by some given function. Firstly, we construct graph-instances on which weak PPSZ has savings of at most (2 + epsilon)/k: the saving of an algorithm on an input formula with n variables is the largest gamma such that the algorithm succeeds (i.e. finds a satisfying assignment) with probability at least 2^{- (1 - gamma) n}. Since PPSZ (both weak and strong) is known to have savings of at least (pi^2 + o(1))/6k, this is optimal up to the constant factor.

Název v anglickém jazyce

Tighter Hard Instances for PPSZ

Popis výsledku anglicky

We construct uniquely satisfiable k-CNF formulas that are hard for the PPSZ algorithm, the currently best known algorithm solving k-SAT. This algorithm tries to generate a satisfying assignment by picking a random variable at a time and attempting to derive its value using some inference heuristic and otherwise assigning a random value. The weak PPSZ checks all subformulas of a given size to derive a value and the strong PPSZ runs resolution with width bounded by some given function. Firstly, we construct graph-instances on which weak PPSZ has savings of at most (2 + epsilon)/k: the saving of an algorithm on an input formula with n variables is the largest gamma such that the algorithm succeeds (i.e. finds a satisfying assignment) with probability at least 2^{- (1 - gamma) n}. Since PPSZ (both weak and strong) is known to have savings of at least (pi^2 + o(1))/6k, this is optimal up to the constant factor.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

ISBN

978-3-95977-041-5

ISSN

1868-8969

e-ISSN

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Počet stran výsledku

13

Strana od-do

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Název nakladatele

Schloss Dagstuhl, Leibniz-Zentrum für Informatik

Místo vydání

Dagstuhl

Místo konání akce

Warsaw

Datum konání akce

10. 7. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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