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Circuit satisfiability and constraint satisfaction around Skolem arithmetic.

Glaßer, Christian and Jonsson, Peter and Martin, Barnaby (2017) 'Circuit satisfiability and constraint satisfaction around Skolem arithmetic.', Theoretical computer science., 703 . pp. 18-36.


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;×), 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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2017 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:31 August 2017
Date deposited:12 September 2017
Date of first online publication:06 September 2017
Date first made open access:06 September 2018

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