Model Checking for a Class of Weighted Automata

Abstract

A large number of different model checking approaches has been proposed during the last decade. The different approaches are applicable to different model types including untimed, timed, probabilistic and stochastic models. This paper presents a new framework for model checking techniques which includes some of the known approaches and enlarges the class of models to which model checking can be applied to the general class of weighted automata. The approach allows an easy adaption of model checking to models which have not been considered yet for this purpose. Examples for those new model types for which model checking can be applied are max/plus or min/plus automata which are well established models to describe different forms of dynamic systems and optimization problems. In this context, model checking can be used to verify temporal or quantitative properties of a system. The paper first presents briefly our class of weighted automata, as a very general model type. Then Valued Computational Tree Logic (CTL$) is introduced as a natural extension of the well known branching time logic CTL. Afterwards, algorithms to check a weighted automaton with respect to a CTL$ formula are presented. As a last result, bisimulation equivalence is extended to weighted automata and CTL$.