The complexity of satisfaction problems in reverse mathematics

Ludovic Patey 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
Inria de Paris, CNRS - Centre National de la Recherche Scientifique, UPD7 - Université Paris Diderot - Paris 7, PPS - Preuves, Programmes et Systèmes
Abstract : Satisfiability problems play a central role in computer science and engineering as a general framework for studying the complexity of various problems. Schaefer proved in 1978 that truth satisfaction of propositional formulas given a language of relations is either NP-complete or tractable. We classify the corresponding satisfying assignment construction problems in the framework of reverse mathematics and show that the principles are either provable over RCA 0 or equivalent to WKL 0. We formulate also a Ramseyan version of the problems and state a different dichotomy theorem. However, the different classes arising from this classification are not known to be distinct.
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Ludovic Patey. The complexity of satisfaction problems in reverse mathematics. Lecture Notes in Computer Science, Springer, 2015, 4 (1), pp.69-84. ⟨hal-01888582⟩

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