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Weighted Bisimulation in Linear Algebraic Form

  • Conference paper
CONCUR 2009 - Concurrency Theory (CONCUR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5710))

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Abstract

We study bisimulation and minimization for weighted automata, relying on a geometrical representation of the model, linear weighted automata (lwa). In a lwa, the state-space of the automaton is represented by a vector space, and the transitions and weighting maps by linear morphisms over this vector space. Weighted bisimulations are represented by sub-spaces that are invariant under the transition morphisms. We show that the largest bisimulation coincides with weighted language equivalence, can be computed by a geometrical version of partition refinement and that the corresponding quotient gives rise to the minimal weighted-language equivalence automaton. Relations to Larsen and Skou’s probabilistic bisimulation and to classical results in Automata Theory are also discussed.

Work partially supported by eu within the fet-GC2 initiative, project Sensoria.

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Author information

Authors and Affiliations

  1. Dipartimento di Sistemi e Informatica, Università di Firenze, Viale Morgagni 65, I-50134, Firenze

    Michele Boreale

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  1. Michele Boreale
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Bologna, Mura A. Zamboni 7, 40127, Bologna, Italy

    Mario Bravetti  & Gianluigi Zavattaro  & 

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Boreale, M. (2009). Weighted Bisimulation in Linear Algebraic Form. In: Bravetti, M., Zavattaro, G. (eds) CONCUR 2009 - Concurrency Theory. CONCUR 2009. Lecture Notes in Computer Science, vol 5710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04081-8_12

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  • DOI: https://doi.org/10.1007/978-3-642-04081-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04080-1

  • Online ISBN: 978-3-642-04081-8

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