Journal of Symbolic Logic
Handbook of combinatorics (vol. 2)
Closure properties of constraints
Journal of the ACM (JACM)
Building tractable disjunctive constraints
Journal of the ACM (JACM)
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Relation Algebras and their Application in Temporal and Spatial Reasoning
Artificial Intelligence Review
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Constraint Satisfaction with Countable Homogeneous Templates
Journal of Logic and Computation
The Complexity of Equality Constraint Languages
Theory of Computing Systems
Constraint Satisfaction Problems with Infinite Templates
Complexity of Constraints
Maximal infinite-valued constraint languages
Theoretical Computer Science
Qualitative CSP, finite CSP, and SAT: comparing methods for qualitative constraint-based reasoning
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
The complexity of temporal constraint satisfaction problems
Journal of the ACM (JACM)
A fast algorithm and datalog inexpressibility for temporal reasoning
ACM Transactions on Computational Logic (TOCL)
Proceedings of the forty-third annual ACM symposium on Theory of computing
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Proceedings of the forty-third annual ACM symposium on Theory of computing
SIAM Journal on Discrete Mathematics
Hi-index | 0.00 |
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in polynomial time, or is NP-complete. We present an analog of this dichotomy result for the propositional logic of graphs instead of Boolean logic. In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction Phi of statements ("constraints") about these variables in the language of graphs, where each statement is taken from a fixed finite set Psi of allowed quantifier-free first-order formulas; the question is whether Phi is satisfiable in a graph. We prove that either Psi is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time, or the problem is NP-complete. This is achieved by a universal-algebraic approach, which in turn allows us to use structural Ramsey theory. To apply the universal-algebraic approach, we formulate the computational problems under consideration as constraint satisfaction problems (CSPs) whose templates are first-order definable in the countably infinite random graph. Our method to classify the computational complexity of those CSPs produces many statements of independent mathematical interest.