Spines of Random Constraint Satisfaction Problems: Definition and Connection with Computational Complexity
We prove a result displaying a connection between the existence of a phase transition in combinatorial problems and the complexity of decision algorithms. Specifically, for the class of generalized random satisfiability problems we prove that a discontinuity in a variant (called spine) of the order parameter used in the study of phase transitions in such problems is accompanied by an exponential lower bound on the complexity of resolution proofs
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