Complexity of Model Checking over General Linear Time

Abstract

Temporal logics over general linear time allow us to capture continuous properties in applications such as distributed systems, natural language, message passing and A.I. modelling of human reasoning. Linear time structures, however, can exhibit a wide range of behaviours that are hard to reason with, or even describe finitely. Recently, a formal language of Model Expressions has been proposed to allow the convenient finite description of an adequately representative range of these generally infinite structures. Given a model described in this Model Expression language and a temporal logic formula, a model checking algorithm decides whether the formula is satisfied at some time in the model. Tools based on such algorithms would support a wide variety of tasks such as verification and counter-example investigation. A previous paper gave an exponential space algorithm for the problem of model checking Until/Since temporal formulas over linear time Model Expressions. Here we prove that the problem is actually PSPACE-complete. We present a new PSPACE algorithm and we show PSPACE-hardness by a reduction from quantified boolean formulas.