Generating models of a matched formula with a polynomial delay

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10331417" target="_blank" >RIV/00216208:11320/16:10331417 - isvavai.cz</a>

Výsledek na webu

<a href="http://isaim2016.cs.virginia.edu/papers/ISAIM2016_Boolean_Savicky_Kucera.pdf" target="_blank" >http://isaim2016.cs.virginia.edu/papers/ISAIM2016_Boolean_Savicky_Kucera.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Generating models of a matched formula with a polynomial delay

Popis výsledku v původním jazyce

A matched formula is a CNF formula, such that the system of the sets of the variables, which appear in individual clauses, has a system of distinct representatives. Such a formula is always satisfiable. Matched formulas are used, for example, in the area of parametrized complexity. We prove that the problem of counting the number of the models (satisfying assignments) of a matched formula is #P-complete. On the other hand, we define a class of formulas generalizing the matched formulas and prove that for a formula in this class, one can choose in polynomial time a variable suitable for splitting the tree for the search of the models of the formula. As a consequence, the models of a formula from this class, in particular of any matched formula, can be generated sequentially with a delay polynomial in the size of the input. On the other hand, we prove that this task cannot be performed efficiently for the linearly satisfiable formulas, which is a generalization of matched formulas containing the class considered above.

Název v anglickém jazyce

Generating models of a matched formula with a polynomial delay

Popis výsledku anglicky

A matched formula is a CNF formula, such that the system of the sets of the variables, which appear in individual clauses, has a system of distinct representatives. Such a formula is always satisfiable. Matched formulas are used, for example, in the area of parametrized complexity. We prove that the problem of counting the number of the models (satisfying assignments) of a matched formula is #P-complete. On the other hand, we define a class of formulas generalizing the matched formulas and prove that for a formula in this class, one can choose in polynomial time a variable suitable for splitting the tree for the search of the models of the formula. As a consequence, the models of a formula from this class, in particular of any matched formula, can be generated sequentially with a delay polynomial in the size of the input. On the other hand, we prove that this task cannot be performed efficiently for the linearly satisfiable formulas, which is a generalization of matched formulas containing the class considered above.

Druh

O - Ostatní výsledky

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GA15-15511S" target="_blank" >GA15-15511S: Booleovské techniky v reprezentaci znalostí</a><br>

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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