DRAT proofs, propagation redundancy, and extended resolution

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

DRAT proofs, propagation redundancy, and extended resolution

Original language description

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 $${}^-$$.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

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

Project

<a href="/en/project/GA19-05497S" target="_blank" >GA19-05497S: Complexity of mathematical proofs and structures</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

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

Article name in the collection

Theory and Applications of Satisfiability Testing – SAT 2019

ISBN

978-3-030-24257-2

ISSN

0302-9743

e-ISSN

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Number of pages

19

Pages from-to

71-89

Publisher name

Springer

Place of publication

Cham

Event location

Lisbon

Event date

Jul 9, 2019

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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