The complexity of weak unification of bounded simple set terms

In this paper we consider the problem of weak unification of bounded simple set terms. Simple set terms are of the form {e1, ..., en}, where ei is a constant or a variable and are much used in deductive database systems such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{L}\mathcal{D}\mathcal{L}$$ \end{document}and Coral. We consider a restricted form of unification, called “weak unification”, which is mainly used in the field of deductive databases where the database may contain both constants and variables and the program is “safe”. The main result of the paper is the detailed complexity analysis of the weak unification problem by providing a formula for determining the number of weak unifiers.