In between resolution and cutting planes: A study of proof systems for pseudo-boolean SAT solving

Marc Vinyals, Jan Elffers, Jesús Giráldez-Cru, Stephan Gocht, Jakob Nordström

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13 Citeringar (SciVal)

Sammanfattning

We initiate a proof complexity theoretic study of subsystems of cutting planes (CP) modelling proof search in conflict-driven pseudo-Boolean (PB) solvers. These algorithms combine restrictions such as that addition of constraints should always cancel a variable and/or that so-called saturation is used instead of division. It is known that on CNF inputs cutting planes with cancelling addition and saturation is essentially just resolution. We show that even if general addition is allowed, this proof system is still polynomially simulated by resolution with respect to proof size as long as coefficients are polynomially bounded. As a further way of delineating the proof power of subsystems of CP, we propose to study a number of easy (but tricky) instances of problems in NP. Most of the formulas we consider have short and simple tree-like proofs in general CP, but the restricted subsystems seem to reveal a much more varied landscape. Although we are not able to formally establish separations between different subsystems of CP—which would require major technical breakthroughs in proof complexity—these formulas appear to be good candidates for obtaining such separations. We believe that a closer study of these benchmarks is a promising approach for shedding more light on the reasoning power of pseudo-Boolean solvers.

Originalspråkengelska
Titel på gästpublikationTheory and Applications of Satisfiability Testing – SAT 2018
Undertitel på gästpublikation 21st International Conference, SAT 2018, Held as Part of the Federated Logic Conference, FloC 2018, Proceedings
RedaktörerOlaf Beyersdorff, Christoph M. Wintersteiger
FörlagSpringer
Sidor292-310
Antal sidor19
ISBN (tryckt)9783319941431
DOI
StatusPublished - 2018
Externt publiceradJa
Evenemang21st International Conference on Theory and Applications of Satisfiability Testing, SAT 2018 Held as Part of the Federated Logic Conference, FloC 2018 - Oxford, Storbritannien
Varaktighet: 2018 jul 92018 jul 12

Publikationsserier

NamnLecture Notes in Computer Science
FörlagSpringer
Volym10929
ISSN (tryckt)0302-9743
ISSN (elektroniskt)1611-3349

Konferens

Konferens21st International Conference on Theory and Applications of Satisfiability Testing, SAT 2018 Held as Part of the Federated Logic Conference, FloC 2018
Land/TerritoriumStorbritannien
OrtOxford
Period2018/07/092018/07/12

Ämnesklassifikation (UKÄ)

  • Datavetenskap (datalogi)

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