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Negative Results on Decidability and Small Model Property of Process Equations

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Book cover Models, Algorithms, Logics and Tools

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10460))

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Abstract

This paper studies the decidability and small model property of process equations of the form

$$\begin{aligned} (P|\varPi _{i=1}^{n}C_i(X_i))\backslash L\equiv (Q|\varPi _{j=1}^{m}D_j(Y_j))\backslash K \end{aligned}$$

where P, Q are finite state processes, \(X_i,Y_j\) are process variables, and \(C_i(X_i)\), \(D_j(Y_j)\) are process expressions linear in \(X_i\) and \(Y_j\) respectively. It shows that, when \(n+m>1\), the equation problem is not decidable and does not have small model property for any equivalence relation \(\equiv \) which is at least as strong as complete trace equivalence but not stronger than strong bisimilarity.

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Acknowledgments

The results reported in this work were obtained more than twenty years ago, from the time when I was a PhD student under the supervision of Kim G. Larsen, to sometime not long after I finished my thesis. To this day I still remember many detailed discussions with Kim about this research, which had given me great inspirations as well as immense pleasure. Kim encouraged me to write a paper about the results and submit it for publication, but somehow the process never got finished. I am very happy that now I can contribute with it to the Festschrift in his honor.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Xinxin Liu

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  1. Xinxin Liu
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Correspondence to Xinxin Liu .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Luca Aceto

  2. Aalborg University, Aalborg, Denmark

    Giorgio Bacci

  3. Aalborg University, Aalborg, Denmark

    Giovanni Bacci

  4. Reykjavík University, Reykjavik, Iceland

    Anna Ingólfsdóttir

  5. Inria Campus Beaulieu, Rennes, France

    Axel Legay

  6. Aalborg University, Aalborg, Denmark

    Radu Mardare

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Liu, X. (2017). Negative Results on Decidability and Small Model Property of Process Equations. In: Aceto, L., Bacci, G., Bacci, G., Ingólfsdóttir, A., Legay, A., Mardare, R. (eds) Models, Algorithms, Logics and Tools. Lecture Notes in Computer Science(), vol 10460. Springer, Cham. https://doi.org/10.1007/978-3-319-63121-9_10

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  • DOI: https://doi.org/10.1007/978-3-319-63121-9_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63120-2

  • Online ISBN: 978-3-319-63121-9

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