Automata-driven efficient subterm unification

Syntactic unification has widespread use in computing. There are several operations used in deductive computing such as critical pair generation, paramodulation and narrowing that require unifying a term s with every subterm of another term p. This subterm unification problem can be solved naively by repeatedly unifying s with each subterm of p in isolation. The drawback of doing unification in isolation is that commonality among subterms of p is ignored. We present an algorithm for efficient subterm unification by exploiting this commonality. The central idea used in our algorithm is to reduce the common part computation in unification into a string-matching problem and solve it efficiently using a string-matching automaton. The automaton succinctly captures the commonality between subterms of p. The string-matching approach, in conjunction with two new techniques called bidirectional-reduce and marking enables efficient unification of s with every subterm of p.