Abstract
In this paper we establish several tight complexity bounds on the sequential and parallel complexity of the associative-commutative (AC) matching problem and its variants. One of our main contributions in this paper is the demonstration of a much tighter relationship between AC matching of linear terms and bipartite matching in both sequential and parallel computation. Another contribution is the use of complexity theoretic techniques to find parallelism in these problems. We believe that this approach can be successfully applied to other matching and unification problems that are not amenable to direct parallelization.
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