Abstract
There is a trend to study extended variants of propositional logic which have explicit means to represent cardinality constraints. That is accomplished using so-called c-atoms. We show that c-atoms can be efficiently reduced to a general form of Exact Satisfiability. The general x i sat problem is to find an assignment for a CNF such that exactly i literals are true in each clause for any i ≥ 1. We show that this problem is solvable in time O(1.4143n) (where n is the number of variables) regardless of i if we allow exponential space. For polynomial space, we present an algorithm solving x i sat for all i strictly better than the trivial O(2n) bound. For i=2, i=3 and i=4 we obtain upper time bounds in O(1.5157n), O(1.6202n) and O(1.6844n), respectively. We also present a dedicated x 2 sat algorithm running in polynomial space and time O(1.4511n).
The research is supported by CUGS – National Graduate School in Computer Science, Sweden.
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Dahllöf, V. (2005). Applications of General Exact Satisfiability in Propositional Logic Modelling. In: Baader, F., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32275-7_7
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DOI: https://doi.org/10.1007/978-3-540-32275-7_7
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