Linear Time Datalog and Branching Time Logic

We survey recent results about the relation between Datalog and temporal veriication logics. Datalog is a well-known database query language relying on the logic programming paradigm. We introduce Dat-alog LITE, a fragment of Datalog with well-founded negation, which has an easy stratiied semantics and a linear time model checking algorithm. Datalog LITE subsumes temporal languages such as CTL and the alternation-free-calculus. We give easy syntactic characterizations of these temporal languages by fragments of Datalog LITE, and show that Datalog LITE has the same expressive power as the alternation-free portion of guarded xed point logic. 1 2 1. INTRODUCTION During the last decade, model checking has become one of the preemi-nent applications of logic in computer science. Temporal model checking is a technique for verifying that a system satisses its speciications by (i) representing the system as a Kripke structure, (ii) writing the spec-iication in a suitable temporal logic, and (iii) algorithmically checking that the Kripke structure is a model of the speciication formula. Model checking has been successfully applied in hardware veriication, and has become an industrial standard tool for hardware design. The main practical problem in model checking is the so-called state explosion problem caused by the fact that the Kripke structure represents the state space of the system under investigation, and thus it is of size exponential in the number of variables. The state explosion problem is alleviated by a number of techniques, in particular symbolic techniques which represent the Kripke structure by Binary Decision Di-and reduction techniques such as the cone of innuence reduction and the partial order reduction. For recent overviews of model checking, we refer the reader to Clarke et al., 2000b; Clarke and Schlingloo, 2000. The temporal logics used in model checking provide a number of important properties which are crucial for the method, distinguish them from many other logics in computer science, and serve as a basis for the above mentioned methods. The most outstanding properties are fast (in fact, often linear time) model checking procedures, decidability of the satissability problem, and structure theorems about the models of temporal formulas such as the tree model property. Some of the most prominent examples of temporal logics are branching time logics such as computational tree logic CTL (Clarke and Emerson, 1981), the modal-calculus L (Kozen, 1983), and its alternation-free fragment L 1. The contribution of this paper is to present Datalog LITE (LInear Time Extended …