Abstract
We present a new randomized parallel algorithm for term matching. Let n be the number of nodes of the directed acyclic graphs (dags) representing the terms to be matched, then our algorithm uses O(log2n) parallel time and M(n) processors, where M(n) is the complexity of n by n matrix multiplication. The number of processors is a significant improvement over previously known bounds. Under various syntactic restrictions on the form of the input dags only O(n2) processors are required in order to achieve deterministic O(log2n) parallel time. Furthermore, we reduce directed graph reachability to term matching using constant parallel time and O(n2) processors. This is strong evidence that in practice, taking M(n) to be n3, no deterministic algorithm can beat the processor bound of our randomized algorithm. We also improve the lower bound of [DKM] on the unification problem. We show that unification is logspace-complete in PTIME even if both input terms are linear, i.e., no variable appears more than once in each term.
Research supported partly by an IBM Faculty Development Award, and partly by NSF grant MCS-8210830.
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Dwork, C., Kanellakis, P., Stockmeyer, L. (1986). Parallel algorithms for term matching. In: Siekmann, J.H. (eds) 8th International Conference on Automated Deduction. CADE 1986. Lecture Notes in Computer Science, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16780-3_109
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DOI: https://doi.org/10.1007/3-540-16780-3_109
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