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International Andrei Ershov Memorial Conference on Perspectives of System Informatics

PSI 2014: Perspectives of System Informatics pp 142–150Cite as

Timed History Preserving Bisimulation and Open Maps

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8974))

Abstract

The open maps approach has recently been successfully applied to structure and unify a wide range of behavior equivalences for concurrency. In this paper, we will prove that timed history preserving (thp-) bisimulation can be captured by an open maps based bisimilarity and its logical counterpart — path bisimilarity, when timed causal trees are chosen as the model category. In particular, we will construct a category of timed causal trees and a subcategory of causal timed words, for which notions of open maps and paths will be developed. Then we will define the open maps based bisimilarity and the path bisimilarity and will establish that the obtained bisimilaries coincide with thp-bisimulation.

This work is supported in part by DFG-RFBR (grant No BE 1267/14-1, grant No 14-01-91334).

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Notes

  1. 1.

    \(\delta [y/x]\) is the substitution of \(y\) for \(x\) in \(\delta \).

  2. 2.

    Here \(\eta ^{-1}(\nu _i)(x')\) \(:=\) \(\nu _i(\eta (x'))\) for all \(x'\in V'\) and \(0\le i \le n\).

  3. 3.

    The number returned by \(I(i,x)\) is the last state before \(i\) at which \(x\) was reset.

  4. 4.

    In our case the initial object \(I\) is the timed causal tree \((\{s_0\},s_0,{\varSigma },\emptyset ,\emptyset ,\emptyset )\).

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Authors and Affiliations

  1. A.P. Ershov Institute of Informatics Systems, SB RAS, 6, Acad. Lavrentiev Avenue, 630090, Novosibirsk, Russia

    Nataliya S. Gribovskaya

Authors
  1. Nataliya S. Gribovskaya
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Correspondence to Nataliya S. Gribovskaya .

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Editors and Affiliations

  1. School of Computer Science, University of Manchester, Manchester, United Kingdom

    Andrei Voronkov

  2. A.P. Ershov Institute of Informatics Systems, Novosibirsk, Russia

    Irina Virbitskaite

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Gribovskaya, N.S. (2015). Timed History Preserving Bisimulation and Open Maps. In: Voronkov, A., Virbitskaite, I. (eds) Perspectives of System Informatics. PSI 2014. Lecture Notes in Computer Science(), vol 8974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46823-4_12

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  • DOI: https://doi.org/10.1007/978-3-662-46823-4_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-46822-7

  • Online ISBN: 978-3-662-46823-4

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