Long Proofs of (Seemingly) Simple Formulas

Forskningsoutput: Kapitel i bok/rapport/Conference proceedingKonferenspaper i proceeding

Abstract

In 2010, Spence and Van Gelder presented a family of CNF formulas based on combinatorial block designs. They showed empirically that this construction yielded small instances that were orders of magnitude harder for state-of-the-art SAT solvers than other benchmarks of comparable size, but left open the problem of proving theoretical lower bounds. We establish that these formulas are exponentially hard for resolution and even for polynomial calculus, which extends resolution with algebraic reasoning. We also present updated experimental data showing that these formulas are indeed still hard for current CDCL solvers, provided that these solvers do not also reason in terms of cardinality constraints (in which case the formulas can become very easy). Somewhat intriguingly, however, the very hardest instances in practice seem to arise from so-called fixed bandwidth matrices, which are provably easy for resolution and are also simple in practice if the solver is given a hint about the right branching order to use. This would seem to suggest that CDCL with current heuristics does not always search efficiently for short resolution proofs, despite the theoretical results of [Pipatsrisawat and Darwiche 2011] and [Atserias, Fichte, and Thurley 2011].

Detaljer

Författare
Externa organisationer
  • KTH Royal Institute of Technology
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)
Originalspråkengelska
Titel på värdpublikationTheory and Applications of Satisfiability Testing, SAT 2014
Undertitel på gästpublikation17th International Conference, Held as Part of theVienna Summer of Logic, VSL 2014, Proceedings
FörlagSpringer
Sidor121-137
Antal sidor17
ISBN (tryckt)9783319092836
StatusPublished - 2014
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa
Evenemang17th International Conference on Theory and Applications of Satisfiability Testing, SAT 2014, Held as Part of the Vienna Summer of Logic, VSL 2014 - Vienna, Österrike
Varaktighet: 2014 jul 142014 jul 17

Publikationsserier

NamnLecture Notes in Computer Science
Volym8561
ISSN (tryckt)0302-9743
ISSN (elektroniskt)1611-3349

Konferens

Konferens17th International Conference on Theory and Applications of Satisfiability Testing, SAT 2014, Held as Part of the Vienna Summer of Logic, VSL 2014
LandÖsterrike
OrtVienna
Period2014/07/142014/07/17