DRAT proofs, propagation redundancy, and extended resolution

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00507739" target="_blank" >RIV/67985840:_____/19:00507739 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-030-24258-9_5" target="_blank" >http://dx.doi.org/10.1007/978-3-030-24258-9_5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-24258-9_5" target="_blank" >10.1007/978-3-030-24258-9_5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

DRAT proofs, propagation redundancy, and extended resolution

Popis výsledku v původním jazyce

We study the proof complexity of RAT proofs and related systems including BC, SPR, and PR which use blocked clauses and (subset) propagation redundancy. These systems arise in satisfiability (SAT) solving, and allow inferences which preserve satisfiability but not logical implication. We introduce a new inference SR using substitution redundancy. We consider systems both with and without deletion. With new variables allowed, the systems are known to have the same proof theoretic strength as extended resolution. We focus on the systems that do not allow new variables to be introduced. Our first main result is that the systems DRAT $${}^-$$, DSPR $${}^-$$ and DPR $${}^-$$, which allow deletion but not new variables, are polynomially equivalent. By earlier work of Kiesl, Rebola-Pardo and Heule, they are also equivalent to DBC $${}^-$$. Without deletion and without new variables, we show that SPR $${}^-$$ can polynomially simulate PR $${}^-$$ provided only short clauses are inferred by SPR inferences. Our next main results are that many of the well-known “hard” principles have polynomial size SPR $${}^-$$ refutations (without deletions or new variables). These include the pigeonhole principle, bit pigeonhole principle, parity principle, Tseitin tautologies, and clique-coloring tautologies, SPR $${}^-$$ can also handle or-fication and xor-ification. Our final result is an exponential size lower bound for RAT $${}^-$$ refutations, giving exponential separations between RAT $${}^-$$ and both DRAT $${}^-$$ and SPR $${}^-$$.

Název v anglickém jazyce

DRAT proofs, propagation redundancy, and extended resolution

Popis výsledku anglicky

We study the proof complexity of RAT proofs and related systems including BC, SPR, and PR which use blocked clauses and (subset) propagation redundancy. These systems arise in satisfiability (SAT) solving, and allow inferences which preserve satisfiability but not logical implication. We introduce a new inference SR using substitution redundancy. We consider systems both with and without deletion. With new variables allowed, the systems are known to have the same proof theoretic strength as extended resolution. We focus on the systems that do not allow new variables to be introduced. Our first main result is that the systems DRAT $${}^-$$, DSPR $${}^-$$ and DPR $${}^-$$, which allow deletion but not new variables, are polynomially equivalent. By earlier work of Kiesl, Rebola-Pardo and Heule, they are also equivalent to DBC $${}^-$$. Without deletion and without new variables, we show that SPR $${}^-$$ can polynomially simulate PR $${}^-$$ provided only short clauses are inferred by SPR inferences. Our next main results are that many of the well-known “hard” principles have polynomial size SPR $${}^-$$ refutations (without deletions or new variables). These include the pigeonhole principle, bit pigeonhole principle, parity principle, Tseitin tautologies, and clique-coloring tautologies, SPR $${}^-$$ can also handle or-fication and xor-ification. Our final result is an exponential size lower bound for RAT $${}^-$$ refutations, giving exponential separations between RAT $${}^-$$ and both DRAT $${}^-$$ and SPR $${}^-$$.

Druh

D - Stať ve sborníku

CEP obor

—

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/GA19-05497S" target="_blank" >GA19-05497S: Složitost matematických důkazů a struktur</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název statě ve sborníku

Theory and Applications of Satisfiability Testing – SAT 2019

ISBN

978-3-030-24257-2

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

19

Strana od-do

71-89

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Lisbon

Datum konání akce

9. 7. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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