Datalog on infinite structures

Datalog is the relational variant of logic programming and has become a standard query language in database theory. The (program) complexity of datalog in its main context so far, on finite databases, is well known to be in EXPTIME. We research the complexity of datalog on infinite databases, motivated by possible applications of datalog to infinite structures (e.g. linear orders) in temporal and spatial reasoning on one hand and the upcoming interest in infinite structures in problems related to datalog, like constraint satisfaction problems: Unlike datalog on finite databases, on infinite structures the computations may take infinitely long, leading to the undecidability of datalog on some infinite structures. But even in the decidable cases datalog on infinite structures may have arbitrarily high complexity, and because of this result, we research some structures with the lowest complexity of datalog on infinite structures: Datalog on linear orders (also dense or discrete, with and without constants, even colored) and tree orders has EXPTIME-complete complexity. To achieve the upper bound on these structures, we introduce a tool set specialized for datalog on orders: Order types, distance types and type disjoint programs. The type concept yields a finite representation of the infinite program results, which could also be of interest for practical applications. We create special type disjoint versions of the programs allowing to solve datalog without the recursion inherent in each datalog program. A transfer of our methods shows that constraint satisfaction problems on infinite structures occur with arbitrarily high time complexity, like datalog.