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Model Checking for a Class of Weighted Automata

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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$.

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Notes

  1. The proposed approach is based on earlier but unpublished work (Buchholz and Kemper 2003a) where a first version of CTL$ has been developed. Compared to Buchholz and Kemper (2003a) the current paper is more complete, several errors have been corrected and more general algorithms for model checking have been developed.

  2. Since the state space is isomorphic to the set of integers {0,...,n − 1}, we use this notation for the set of states, whenever possible.

  3. This is sometimes denoted as a substochastic matrix without traps.

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Authors and Affiliations

  1. Informatik IV, TU Dortmund, 44221, Dortmund, Germany

    Peter Buchholz

  2. Department of Computer Science, College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Peter Kemper

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  1. Peter Buchholz
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  2. Peter Kemper
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Correspondence to Peter Buchholz.

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Buchholz, P., Kemper, P. Model Checking for a Class of Weighted Automata. Discrete Event Dyn Syst 20, 103–137 (2010). https://doi.org/10.1007/s10626-008-0057-0

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