Verifying Temporal Properties in Real Models

Based on pioneering work of Läuchli and Leonard in the 1960s, a novel and expressive formal language, Model Expressions, for describing the compositional construction of general linear temporal structures has recently been proposed. A sub-language, Real Model Expressions, is capable of specifying models over the real flow of time but its semantics are subtly different because of the specific properties of the real numbers. Model checking techniques have been developed for the general linear Model Expressions and it was shown that checking temporal formulas against structures described in the formal language is PSPACE-Complete and linear in the length of the model expression. In this paper we present a model checker for temporal formulas over real-flowed models. In fact the algorithm, and so its complexity, is the same as for the general linear case. To show that this is adequate, we use a concept of temporal bisimulations and establish that it is respected by the compositional construction method. We can then check the correctness of using the general linear model checking algorithm when applied to real model expressions with their special semantics on real-flowed structures.