ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
Handbook of logic in artificial intelligence and logic programming
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Complexity-theoretic models of phase transitions in search problems
Theoretical Computer Science
Combinatorial Algorithms: For Computers and Hard Calculators
Combinatorial Algorithms: For Computers and Hard Calculators
Solution of the Robbins Problem
Journal of Automated Reasoning
Computational Complexity of Simultaneous Elementary Matching Problems
Journal of Automated Reasoning
A Compiler for Rewrite Programs in Associative-Commutative Theories
PLILP '98/ALP '98 Proceedings of the 10th International Symposium on Principles of Declarative Programming
Random 3-SAT: The Plot Thickens
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
FM '99 Proceedings of the Wold Congress on Formal Methods in the Development of Computing Systems-Volume II
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
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AC-matching is the problem of deciding whether an equation involving a binary associative-commutative function symbol, formal variables and formal constants has a solution. This problem is known to be strong NP-complete and to play a fundamental role in equational unification and automated deduction. We initiate an investigation of the existence of a phase transition in random AC-matching and its relationship to the performance of AC-matching solvers.We identify a parameter that captures the "constrainedness" of AC-matching, carry out largescale experiments, and then apply finite-size scaling methods to draw conclusions from the experimental data gathered. Our findings suggest that there is a critical value of the parameter at which the asymptotic probability of solvability of random AC-matching changes from 1 to 0. Unlike other NP-complete problems, however, the phase transition in random AC-matching seems to emerge very slowly, as evidenced by the experimental data and also by the rather small value of the scaling exponent in the power law of the derived finite-size scaling transformation.