Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
The phase transition in 1-in-k SAT and NAE 3-SAT
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
The Gn,mphase transition is not hard for the Hamiltonian cycle problem
Journal of Artificial Intelligence Research
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We consider questions such as what is the complexity of recognizing instances of (monotonic) NP-complete problems in which no variable is fixed (or frozen) by the set of solutions. Since this unfrozenness is also a monotonic property in NP, this leads to an inductive sequence of properties for each monotone NP-complete property. In some cases the sequence remains NP-complete, while in others it at some point enters P. Determining the boundaries is particularly challenging. We also consider the related questions of recognizing maximal properties. This study was motivated by results from statistical mechanics being applied to phase transitions of NP-complete problems, which show a correlation of hard instances with a sudden increase in frozen variables.