Circuit satisfiability and constraint satisfaction around Skolem Arithmetic

• We study interactions between Skolem Arithmetic and certain classes of Circuit Satisfiability and Constraint Satisfaction Problems (CSPs). We revisit results of Glasser et al. [1] in the context of CSPs and settle the major open question from that paper, finding a certain satisfiability problem on circuits-involving complement, intersection, union and multiplication-to be decidable. This we prove using the decidability of Skolem Arithmetic. Then we solve a second question left open in [1] by proving a tight upper bound for the similar circuit satisfiability problem involving just intersection, union and multiplication. We continue by studying first-order expansions of Skolem Arithmetic without constants, (N; x), as CSPs. We find already here a rich landscape of problems with non-trivial instances that are in P as well as those that are NP-complete. (C) 2017 Elsevier B.V. All rights reserved.

Ämnesord

NATURVETENSKAP  -- Matematik -- Diskret matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Discrete Mathematics (hsv//eng)

Nyckelord

Circuit satisfiability; Constraint satisfaction; Skolem Arithmetic; Computational complexity

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