Rapport de stage de recherche Complexity of Decision Problems in Computational Logic RAPPORT NON CONFIDENTIEL

This report presents the study of algorithms whose goal is to determine whether two Datalog programs are equivalent. Datalog is a query language used over deductive databases. Datalog is a fragment of Prolog, and consists in Horn clauses without function symbols. In general, it is undecidable whether two given Datalog programs are equivalent one to each other; however, this problem becomes decidable if we look at restricted classes of Datalog programs: monadic Datalog programs and transitive Datalog programs. Indeed, the algorithms designed in order to solve the equivalence problem of such Datalog programs involve similar techniques. This report first presents Datalog programs in general, then the two particular classes of Datalog programs above mentioned. It continues with a study of the links between Datalog programs,a finite trees and finite automata. It eventually presents the algorithms designed during the internship, which solve a problem slightly more general than the equivalence problem: the inclusion of a Datalog program in a monadic Datalog program, then in a transitive Datalog program.