On relating CTL to Datalog

CTL is the dominant temporal specification language in practice mainly due to the fact that it admits model checking in linear time. Logic programming and the database query language Datalog are often used as an implementation platform for logic languages. In this paper we present the exact relation between CTL and Datalog and moreover we build on this relation and known efficient algorithms for CTL to obtain efficient algorithms for fragments of stratified Datalog. The contributions of this paper are: a) We embed CTL into STD which is a proper fragment of stratified Datalog. Moreover we show that STD expresses exactly CTL -- we prove that by embedding STD into CTL. Both embeddings are linear. b) CTL can also be embedded to fragments of Datalog without negation. We define a fragment of Datalog with the successor build-in predicate that we call TDS and we embed CTL into TDS in linear time. We build on the above relations to answer open problems of stratified Datalog. We prove that query evaluation is linear and that containment and satisfiability problems are both decidable. The results presented in this paper are the first for fragments of stratified Datalog that are more general than those containing only unary EDBs.Comment: 34 pages, 1 figure (file .eps

The Monadic Second-order Logic Evaluation Problem on Finite Colored Trees: a Database-theoretic Approach

We model the monadic second-order logic (MSO) evaluation problem on finite colored trees in a purely database theoretic framework, based on the well-known MSO-automata connection: we reduce the problem to an acyclic conjunctive query evaluation problem on the one hand and to a monadic datalog evaluation problem on the other hand. This approach offers the possibility to solve the MSO problem using optimized evaluation methods for relational algebra expressions and for datalog programs (such as Yannakakis algorithm [27] and the rewriting method using resolution-based filtering referred to as “magic sets” method in [3]): we use these methods for evaluating our queries and giving estimates of their complexity. This is the first time, to our knowledge, that a solution to the MSO evaluation problem related to relational algebra is given; furthermore, thanks to this reduction, we prove that the automata-based algorithm given in [8] constitutes a particular “instance” of Yannakakis algorithm. Besides the optimized database methods that we propose for solving the MSO evaluation problem, our results prove that MSO-definable queries over colored trees are datalog-definable; this result subsumes the corresponding result in [12] which states that unary MSO queries are monadic datalog-definable and it also subsumes the well-known result that any MSO-definable class of trees is monadic datalog-definable