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What we can learn from conflicts in propositional satisfiability

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Abstract

Learning is a general concept, playing an important role in many Artificial intelligence domains. In this paper, we address the learning paradigm used to explain failures or conflicts encountered during search. This explanation, derived by conflict analysis, and generally expressed as a new constraint, is usually used to dynamically avoid future occurrences of similar situations. Before focusing on clause learning in Boolean satisfiability (SAT), we first overview some important works on this powerful reasoning tool in other domains such as constraint satisfaction and truth maintenance systems. Then, we present a comprehensive survey of the most important works having led to what is called today—conflict driven clause learning—which is one of the key components of modern SAT solvers. We also overview some of the original extensions or variants of clauses learning. In theory, current SAT solvers with clause learning are as powerful as general resolution proof systems. In practice, real-world SAT instances with millions of variables and clauses are now in the scope of this solving paradigm.

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Authors and Affiliations

  1. Microsoft Research, Cambridge, UK

    Youssef Hamadi

  2. LIX École Polytechnique, 91128, Palaiseau, France

    Youssef Hamadi

  3. CRIL-CNRS, Université Lille Nord de France - Artois, Rue Jean Souvraz SP18, 62307, Lens Cedex, France

    Saïd Jabbour & Lakhdar Saïs

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  1. Youssef Hamadi
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  2. Saïd Jabbour
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  3. Lakhdar Saïs
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Correspondence to Lakhdar Saïs.

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This is an updated version of the paper “Learning from Conflicts in Propositional Satisfiability” that appeared in 4OR, 10(1), 15–32 (2012).

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Hamadi, Y., Jabbour, S. & Saïs, L. What we can learn from conflicts in propositional satisfiability. Ann Oper Res 240, 13–37 (2016). https://doi.org/10.1007/s10479-015-2028-9

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