NP is as easy as detecting unique solutions
Theoretical Computer Science
The complexity of facets resolved
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Security-control methods for statistical databases: a comparative study
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On the complexity of H-coloring
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Reasoning about qualitative temporal information
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Closure properties of constraints
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On the algebraic structure of combinatorial problems
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Conjunctive-query containment and constraint satisfaction
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Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
The scaling window of the 2-SAT transition
Random Structures & Algorithms
The complexity of maximal constraint languages
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Some optimal inapproximability results
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Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems
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A Dichotomy Theorem for Constraints on a Three-Element Set
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Functions of multiple-valued logic and the complexity of constraint satisfaction: A short survey
ISMVL '03 Proceedings of the 33rd International Symposium on Multiple-Valued Logic
The Complexity of Homomorphism and Constraint Satisfaction Problems Seen from the Other Side
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Bi-arc graphs and the complexity of list homomorphisms
Journal of Graph Theory
Backbone fragility and the local search cost peak
Journal of Artificial Intelligence Research
Clustering at the phase transition
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Computational complexity of auditing finite attributes in statistical databases
Journal of Computer and System Sciences
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
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A weighted CSP approach to cost-optimal planning
AI Communications
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In constraint satisfaction problems over finite domains, some variables can be frozen, that is, they take the same value in all possible solutions. We study the complexity of the problem of recognizing frozen variables with restricted sets of constraint relations allowed in the instances. We show that the complexity of such problems is determined by certain algebraic properties of these relations. Under the assumption that NP ≠ coNP (and consequently PTIME ≠ NP), we characterize all tractable problems, and describe large classes of NP-complete, coNP-complete, and DP-complete problems. As an application of these results, we completely classify the complexity of the problem in two cases: (1) with domain size 2; and (2) when all unary relations are present. We also give a rough classification for domain size 3.