Relating proof complexity measures and practical hardness of SAT

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Boolean satisfiability (SAT) solvers have improved enormously in performance over the last 10-15 years and are today an indispensable tool for solving a wide range of computational problems. However, our understanding of what makes SAT instances hard or easy in practice is still quite limited. A recent line of research in proof complexity has studied theoretical complexity measures such as length, width, and space in resolution, which is a proof system closely related to state-of-the-art conflict-driven clause learning (CDCL) SAT solvers. Although it seems like a natural question whether these complexity measures could be relevant for understanding the practical hardness of SAT instances, to date there has been very limited research on such possible connections. This paper sets out on a systematic study of the interconnections between theoretical complexity and practical SAT solver performance. Our main focus is on space complexity in resolution, and we report results from extensive experiments aimed at understanding to what extent this measure is correlated with hardness in practice. Our conclusion from the empirical data is that the resolution space complexity of a formula would seem to be a more fine-grained indicator of whether the formula is hard or easy than the length or width needed in a resolution proof. On the theory side, we prove a separation of general and tree-like resolution space, where the latter has been proposed before as a measure of practical hardness, and also show connections between resolution space and backdoor sets.


Externa organisationer
  • University of Helsinki
  • Technion - Israel Institute of Technology
  • KTH Royal Institute of Technology
  • University of Oxford

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)
Titel på värdpublikationPrinciples and Practice of Constraint Programming
Undertitel på gästpublikation18th International Conference, CP 2012, Proceedings
Antal sidor16
ISBN (tryckt)9783642335570
StatusPublished - 2012
Peer review utfördJa
Externt publiceradJa
Evenemang18th International Conference on Principles and Practice of Constraint Programming, CP 2012 - Quebec City, QC, Kanada
Varaktighet: 2012 okt 82012 okt 12


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


Konferens18th International Conference on Principles and Practice of Constraint Programming, CP 2012
OrtQuebec City, QC