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Optimal Zielonka-Type Construction of Deterministic Asynchronous Automata

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Automata, Languages and Programming (ICALP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6199))

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Abstract

Asynchronous automata are parallel compositions of finite-state processes synchronizing over shared variables. A deep theorem due to Zielonka says that every regular trace language can be represented by a deterministic asynchronous automaton. In this paper we improve the construction, in that the size of the obtained asynchronous automaton is polynomial in the size of a given DFA and simply exponential in the number of processes. We show that our construction is optimal within the class of automata produced by Zielonka-type constructions. In particular, we provide the first non trivial lower bound on the size of asynchronous automata.

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References

  1. Baudru, N.: Distributed Asynchronous Automata. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009 - Concurrency Theory. LNCS, vol. 5710, pp. 115–130. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  2. Cori, R., Métivier, Y., Zielonka, W.: Asynchronous mappings and asynchronous cellular automata. Information and Computation 106, 159–202 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Diekert, V., Muscholl, A.: Construction of asynchronous automata. In: Diekert, Rozenberg (eds.) [4], pp. 249–267

    Google Scholar 

  4. Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific, Singapore (1995)

    Google Scholar 

  5. Genest, B., Kuske, D., Muscholl, A.: A Kleene theorem and model checking algorithms for existentially bounded communicating automata. Inf. Comput. 204(6), 920–956 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Genest, B., Muscholl, A.: Constructing Exponential-Size Deterministic Zielonka Automata. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 565–576. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Henriksen, J.G., Mukund, M., Kumar, K.N., Sohoni, M., Thiagarajan, P.S.: A Theory of Regular MSC Languages. Inf. Comput. 202(1), 1–38 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Klarlund, N., Mukund, M., Sohoni, M.: Determinizing Asynchronous Automata. In: Shamir, E., Abiteboul, S. (eds.) ICALP 1994. LNCS, vol. 820, pp. 130–141. Springer, Heidelberg (1994)

    Google Scholar 

  9. Mazurkiewicz, A.: Concurrent Program Schemes and their Interpretations. DAIMI Rep. PB 78, Aarhus University, Aarhus (1977)

    Google Scholar 

  10. Métivier, Y.: An algorithm for computing asynchronous automata in the case of acyclic non-commutation graph. In: Ottmann, T. (ed.) ICALP 1987. LNCS, vol. 267, pp. 226–236. Springer, Heidelberg (1987)

    Google Scholar 

  11. Mukund, M., Kumar, K.N., Sohoni, M.: Synthesizing distributed finite-state systems from MSCs. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 521–535. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Mukund, M., Sohoni, M.: Gossiping, Asynchronous Automata and Zielonka’s Theorem. Report TCS-94-2, School of Mathematics, SPIC Science Foundation, Madras, India (1994)

    Google Scholar 

  13. Mukund, M., Sohoni, M.A.: Keeping Track of the Latest Gossip in a Distributed System. Distributed Computing 10(3), 137–148 (1997)

    Article  Google Scholar 

  14. Stefanescu, A.: Automatic synthesis of distributed transition systems. PhD thesis, Universität Stuttgart (2006)

    Google Scholar 

  15. Zielonka, W.: Notes on finite asynchronous automata. RAIRO–Theoretical Informatics and Applications 21, 99–135 (1987)

    MATH  MathSciNet  Google Scholar 

  16. Zielonka, W.: Safe executions of recognizable trace languages by asynchronous automata. In: Meyer, A.R., Taitslin, M.A. (eds.) Logic at Botik 1989. LNCS, vol. 363, pp. 278–289. Springer, Heidelberg (1989)

    Google Scholar 

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Author information

Authors and Affiliations

  1. CNRS, IPAL UMI, joint with I2R-A*STAR-NUS, Singapore

    Blaise Genest

  2. CNRS, IRISA UMR, joint with Université Rennes I, France

    Blaise Genest

  3. LaBRI, CNRS/Université Bordeaux, France

    Hugo Gimbert, Anca Muscholl & Igor Walukiewicz

Authors
  1. Blaise Genest
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  2. Hugo Gimbert
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  3. Anca Muscholl
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  4. Igor Walukiewicz
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Editor information

Editors and Affiliations

  1. Computing Laboratory, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Samson Abramsky

  2. Université de Bordeaux (LaBRI) & INRIA, 351, cours de la Libération, 33405, Talence Cedex, France,

    Cyril Gavoille

  3. INRIA, Centre de Recherche Bordeaux – Sud-Ouest, 351 cours de la Libération, 33405, Talence Cedex, France

    Claude Kirchner

  4. Heinz Nixdorf Institute, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Friedhelm Meyer auf der Heide

  5. University of Patras and RACTI, 26500, Patras, Greece

    Paul G. Spirakis

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Genest, B., Gimbert, H., Muscholl, A., Walukiewicz, I. (2010). Optimal Zielonka-Type Construction of Deterministic Asynchronous Automata. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14162-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-14162-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14161-4

  • Online ISBN: 978-3-642-14162-1

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