Experiments with Associative-Commutative Discrimination Nets

In [1], we proposed AC-discrimination nets to speed up many-to-one AC-matching. We also proposed secondary automata as a novel data structure to further improve the performance of ACmatching on problems typically arising in practice. In this paper, we present the implementation of AC-discrimination nets within an equational theorem proving system. The implementation exploits the fact that although AC-matching is NP -complete, it can be solved in polynomial time if patterns are restricted to linear terms. It solves the many-to-one AC-matching in two phases. In the first phase, patterns that AC-match modulo nonlinearity the subject are selected. In AC-matching modulo nonlinearity, multiplicities of variable occurrences are ignored in the matching process when computing substitutions for them. The consistency of such substitutions is verified in the second phase for patterns selected from the first phase. Our experimental results provide strong evidence that AC-discrimination nets and secondary automata are indeed useful tools for improving the performance of theorem provers.