Modelling Systems over General Linear Time

Abstract

It has been shown that every temporal logic formula satisfiable over general linear time has a model than can be expressed as a finite Model Expression (ME). The reals are a subclass of general linear time, so similar techniques can be used for the reals. Although MEs are expressive enough for this task, they represent only a single class of elementary equivalent models. In the case where time is represented by integers, regular expressions are equivalent to automata. An ME is more similar to a single run of an automaton than the automaton itself. In linear time it is often useful to model a system as an automaton (or regular expression) rather than a single run of the automaton. In this paper we extend MEs with the operators from Regular Expressions to produce Regular Model Expressions (RegMEs). It is known that model checking temporal logic formulas over MEs is PSPACE-complete. We show that model checking temporal logic formulas over RegMEs is also PSPACE-complete.