Automata-Based Computation of Temporal Equilibrium Models

Temporal Equilibrium Logic (TEL) is a formalism for temporal logic programming that generalizes the paradigm of Answer Set Programming (ASP) introducing modal temporal operators from standard Linear-time Temporal Logic (LTL). In this paper we solve some problems that remained open for TEL like decidability, bounds for computational complexity as well as computation of temporal equilibrium models for arbitrary theories. We propose a method for the latter that consists in building a Büchi automaton that accepts exactly the temporal equilibrium models of a given theory, providing an automata-based decision procedure and illustrating the ω-regularity of such sets. We show that TEL satisfiability can be solved in exponential space and it is hard for polynomial space. Finally, given two theories, we provide a decision procedure to check if they have the same temporal equilibrium models.