Model Checking for a Class of Weighted Automata

TL;DR

This paper introduces a new framework for model checking that extends to weighted automata, including models like max/plus automata, enabling verification of temporal and quantitative properties.

Contribution

It generalizes existing model checking approaches to a broader class of weighted automata, including new types like max/plus automata, with algorithms and bisimulation techniques.

Findings

Framework applicable to various weighted automata types

Algorithms for CTL$ model checking on weighted automata

Bisimulation for weighted automata and CTL$

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, but enlarges the class of models for 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$) is introduced as a natural extension of the well known branching time logic CTL. Afterwards, algorithms to check a weighted automaton according to a CTL$ formula are presented. As a last result, a bisimulation is presented for weighted automata and for CTL$.