Two-sided unification is NP-complete
نویسندگان
چکیده
It is generally accepted that to unify a pair of substitutions θ1 and θ2 means to find out a pair of substitutions η′ and η′′ such that the compositions θ1η ′ and θ2η ′′ are the same. Actually, unification is the problem of solving linear equations of the form θ1X = θ2Y in the semigroup of substitutions. But some other linear equations on substitutions may be also viewed as less common variants of unification problem. In this paper we introduce a two-sided unification as the process of bringing a given substitution θ1 to another given substitution θ2 from both sides by giving a solution to an equation Xθ1Y = θ2. Twosided unification finds some applications in software refactoring as a means for extracting instances of library subroutines in arbitrary pieces of program code. In this paper we study the complexity of two-sided unification and show that this problem is NP-complete by reducing to it the bounded tiling problem.
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