Efficient parallel term matching and anti-unification

In this paper we present optimal processor x time parallel algorithms for term matching and anti-unification of terms represented as trees. Term matching is the special case of unification in which one of the terms is restricted to contain no variables. It has wide applicability to logic programming, term rewriting systems and symbolic pattern matching. Anti-unification is the dual problem of unification in which one computes the most specific generalization of two terms. It has application to inductive inference and theorem proving. Our algorithms run in O(log²N) time using N/log²N processors on a shared-memory model of computation that prohibits simultaneous reads or writes (EREW PRAM). These algorithms are the first polylogarithmic-time EREW algorithms with a processor x time product of the same order as that of their sequential counterparts, thereby permitting optimal speed-ups using any number of processors up to N/log²N. We also use the techniques developed in the paper to provide an N/log N-processor, O(log N)-time algorithm for a shared-memory model that allows both simultaneous reads and simultaneous writes (CRCW PRAM).