DRAT and propagation redundancy proofs without new variables

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00542699" target="_blank" >RIV/67985840:_____/21:00542699 - isvavai.cz</a>

Výsledek na webu

<a href="https://dx.doi.org/10.23638/LMCS-17(2:12)2021" target="_blank" >https://dx.doi.org/10.23638/LMCS-17(2:12)2021</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.23638/LMCS-17(2:12)2021" target="_blank" >10.23638/LMCS-17(2:12)2021</a>

Jazyk výsledku

angličtina

Název v původním jazyce

DRAT and propagation redundancy proofs without new variables

Popis výsledku v původním jazyce

We study the complexity of a range of propositional proof systems which allow inference rules of the form: from a set of clauses Γ derive the set of clauses Γ ∪ {C} where, due to some syntactic condition, Γ ∪ {C} is satisfiable if Γ is, but where Γ does not necessarily imply C. These inference rules include BC, RAT, SPR and PR (respectively short for blocked clauses, resolution asymmetric tautologies, subset propagation redundancy and propagation redundancy), which arose from work in satisfiability (SAT) solving. We introduce a new, more general rule SR (substitution redundancy). If the new clause C is allowed to include new variables then the systems based on these rules are all equivalent to extended resolution. We focus on restricted systems that do not allow new variables. The systems with deletion, where we can delete a clause from our set at any time, are denoted DBC−, DRAT−, DSPR−, DPR− and DSR−. The systems without deletion are BC−, RAT−, SPR−, PR− and SR−. With deletion, we show that DRAT−, DSPR− and DPR− are equivalent. By earlier work of Kiesl, Rebola-Pardo and Heule [KRPH18], they are also equivalent to DBC−. Without deletion, we show that SPR− can simulate PR− provided only short clauses are inferred by SPR inferences. We also show that many of the well-known “hard” principles have small SPR− refutations. 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, and lifting with an index gadget. 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 and propagation redundancy proofs without new variables

Popis výsledku anglicky

We study the complexity of a range of propositional proof systems which allow inference rules of the form: from a set of clauses Γ derive the set of clauses Γ ∪ {C} where, due to some syntactic condition, Γ ∪ {C} is satisfiable if Γ is, but where Γ does not necessarily imply C. These inference rules include BC, RAT, SPR and PR (respectively short for blocked clauses, resolution asymmetric tautologies, subset propagation redundancy and propagation redundancy), which arose from work in satisfiability (SAT) solving. We introduce a new, more general rule SR (substitution redundancy). If the new clause C is allowed to include new variables then the systems based on these rules are all equivalent to extended resolution. We focus on restricted systems that do not allow new variables. The systems with deletion, where we can delete a clause from our set at any time, are denoted DBC−, DRAT−, DSPR−, DPR− and DSR−. The systems without deletion are BC−, RAT−, SPR−, PR− and SR−. With deletion, we show that DRAT−, DSPR− and DPR− are equivalent. By earlier work of Kiesl, Rebola-Pardo and Heule [KRPH18], they are also equivalent to DBC−. Without deletion, we show that SPR− can simulate PR− provided only short clauses are inferred by SPR inferences. We also show that many of the well-known “hard” principles have small SPR− refutations. 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, and lifting with an index gadget. Our final result is an exponential size lower bound for RAT− refutations, giving exponential separations between RAT− and both DRAT− and SPR−.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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

2021

Kód důvěrnosti údajů

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

Název periodika

Logical Methods in Computer Science

ISSN

1860-5974

e-ISSN

1860-5974

Svazek periodika

17

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

31

Strana od-do

12

Kód UT WoS článku

000658731000011

EID výsledku v databázi Scopus

2-s2.0-85105356493