Complexity and Algorithms for the Matching of bag and set terms

Bounded bag and set terms are complex terms in which every element can be a constant or a variable. These types of complex terms have been introduced in several logic languages, such as LDL, Coral and Godel, in order to increase their expressive power, and they have been recently used to define logic languages for database integration. The paper addresses the problem of computing the set of matchers of two bag (or set) terms, by providing a general complexity analysis and a closed formula for determining the number of matchers for tractable cases. An algorithm for the general problem and optimal algorithms for tractable cases are also provided.