On generating all maximal independent sets
Information Processing Letters
Dismantling absolute retracts of reflexive graphs
European Journal of Combinatorics
Clique graphs and Helly graphs
Journal of Combinatorial Theory Series B
Resolution-based theorem proving for many-valued logics
Journal of Symbolic Computation
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Transformations between Signed and Classical Clause Logic
ISMVL '99 Proceedings of the Twenty Ninth IEEE International Symposium on Multiple-Valued Logic
The 2-SAT Problem of Regular Signed CNF Formulas
ISMVL '00 Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic
New Logical and Complexity Results for Signed-SAT
ISMVL '03 Proceedings of the 33rd International Symposium on Multiple-Valued Logic
Constraint Processing
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
2-SAT Problems in Some Multi-Valued Logics Based on Finite Lattices
ISMVL '07 Proceedings of the 37th International Symposium on Multiple-Valued Logic
An algorithm for random signed 3-SAT with intervals
Theoretical Computer Science
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In this paper, we study the problem of satisfiability of Boolean formulas @f in conjunctive normal form (CNF) whose literals have the form v@?S and express the membership of values to sets S of a given set family S defined on a finite domain D. We establish the following dichotomy result. We show that checking the satisfiability of such formulas (called S-formulas) with three or more literals per clause is NP-complete except the trivial case when the intersection of all sets in S is nonempty. On the other hand, the satisfiability of S-formulas @f containing at most two literals per clause is decidable in polynomial time if S satisfies the Helly property, and is NP-complete otherwise (in the first case, we present an O(|@f|@?|S|@?|D|)-time algorithm for deciding if @f is satisfiable). Deciding whether a given set family S satisfies the Helly property can be done in polynomial time. We also overview several well-known examples of Helly families and discuss the consequences of our result to such set families and its relationship with the previous work on the satisfiability of signed formulas in multiple-valued logic.