SAT and SMT are still resolution: questions and challenges

Authors:
Robert Nieuwenhuis
Affiliations:
UPC, Barcelona, Spain
Venue:
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Year:
2012

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Abstract

The aim of this invited talk is to discuss strengths, limitations and challenges around one of the simplest yet most powerful practical automated deduction formalisms, namely propositional SAT and its extensions. We will see some of the reasons why CDCL SAT solvers are so effective for finding solutions to so diverse real-world problems, using a single fully automatic push-button strategy, and, by extending them to SAT Modulo Theories (SMT), also to optimization problems and problems with complex (e.g., arithmetic) constraints for which a full encoding into SAT would be too large and/or inefficient. We will give some examples of trade-offs regarding full SAT encodings vs SMT theory solvers, and discuss why SAT and even SMT are just binary resolution strategies, the consequences of this fact, and possible ways to overcome it. Many aspects of the discussion carry over to first-order logic and beyond.