On the algebraic structure of combinatorial problems
Theoretical Computer Science
Building tractable disjunctive constraints
Journal of the ACM (JACM)
Composition sequences for functions over a finite domain
Theoretical Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
Parameterized Complexity
Complexity of Existential Positive First-Order Logic
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
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Constraint Satisfaction Problems (csp ) constitute a convenient way to capture many combinatorial problems. The general csp is known to be NP-complete, but its complexity depends on a parameter, usually a set of relations, upon which they are constructed. Following the parameter, there exist tractable and intractable instances of csp s. In this paper we show a dichotomy theorem for every finite domain of csp including also disjunctions. This dichotomy condition is based on a simple condition, allowing us to classify monotone csp s as tractable or NP-complete. We also prove that the meta-problem, verifying the tractability condition for monotone constraint satisfaction problems, is fixed-parameter tractable. Moreover, we present a polynomial-time algorithm to answer this question for monotone csp s over ternary domains.