Automata-driven efficient subterm unification

R. Ramesh, I.V. Ramakrishnan, R.C. Sekar
2001 Theoretical Computer Science  
Syntactic uniÿcation 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 uniÿcation problem can be solved naively by repeatedly unifying s with each subterm of p in isolation. The drawback of doing uniÿcation in isolation is that commonality among subterms of p is ignored. We present an algorithm for e cient
more » ... uniÿcation by exploiting this commonality. The central idea used in our algorithm is to reduce the common part computation in uniÿcation into a string-matching problem and solve it e ciently 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 e cient uniÿcation of s with every subterm of p.
doi:10.1016/s0304-3975(99)00131-0 fatcat:aehivjrbhfayhou4k2cgiw42ma