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Transactions on Petri Nets and Other Models of Concurrency XIV pp 146–171Cite as

Kleene Theorems for Free Choice Automata over Distributed Alphabets

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Part of the book series: Lecture Notes in Computer Science ((TOPNOC,volume 11790))

Abstract

We provided (PNSE’2014) expressions for free choice nets having distributed choice property which makes the nets direct product representable. In a recent work (PNSE’2016), we gave equivalent syntax for a larger class of free choice nets obtained by dropping distributed choice property.

In both these works, the classes of free choice nets were restricted by a product condition on the set of final markings. In this paper we do away with this restriction and give expressions for the resultant classes of nets which correspond to free choice synchronous products and Zielonka automata. For free choice nets with distributed choice property, we give an alternative characterization using properties checkable in polynomial time.

Free choice nets we consider are 1-bounded, S-coverable, and are labelled with distributed alphabets, where S-components of the associated S-cover respect the given alphabet distribution.

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Notes

  1. 1.

    A preliminary version of this paper appeared at 14th PNSE workshop, held at Bratislava [16].

References

  1. Antimirov, V.: Partial derivatives of regular expressions and finite automaton constructions. Theoret. Comput. Sci. 155(2), 291–319 (1996)

    Article  MathSciNet  Google Scholar 

  2. Brzozowski, J.A.: Derivatives of regular expressions. J. ACM 11(4), 481–494 (1964)

    Article  MathSciNet  Google Scholar 

  3. Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge University Press, New York (1995)

    Book  Google Scholar 

  4. Garg, V.K., Ragunath, M.: Concurrent regular expressions and their relationship to petri nets. Theoret. Comput. Sci. 96(2), 285–304 (1992)

    Article  MathSciNet  Google Scholar 

  5. Grabowski, J.: On partial languages. Fundam. Inform. 4(2), 427–498 (1981)

    MathSciNet  MATH  Google Scholar 

  6. Hack, M.H.T.: Analysis of production schemata by Petri nets. Project Mac Report TR-94, MIT (1972)

    Google Scholar 

  7. Iordache, M.V., Antsaklis, P.J.: The ACTS software and its supervisory control framework. In: Proceedings Conference on Decision and Control, CDC, pp. 7238–7243. IEEE (2012)

    Google Scholar 

  8. Jantzen, M.: Language theory of Petri nets. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) ACPN 1986. LNCS, vol. 254, pp. 397–412. Springer, Heidelberg (1987). https://doi.org/10.1007/978-3-540-47919-2_15

    Chapter  Google Scholar 

  9. Lodaya, K.: Product automata and process algebra. In: SEFM. IEEE (2006)

    Google Scholar 

  10. Lodaya, K., Mukund, M., Phawade, R.: Kleene theorems for product systems. In: Holzer, M., Kutrib, M., Pighizzini, G. (eds.) DCFS 2011. LNCS, vol. 6808, pp. 235–247. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22600-7_19

    Chapter  MATH  Google Scholar 

  11. Mirkin, B.G.: An algorithm for constructing a base in a language of regular expressions. Eng. Cybern. 5, 110–116 (1966)

    Google Scholar 

  12. Mukund, M.: Automata on distributed alphabets. In: D’Souza, D., Shankar, P. (eds.) Modern Applications of Automata Theory. World Scientific (2011)

    Google Scholar 

  13. Petersen, J.L.: Computation sequence sets. J. Comput. Syst. Sci. 13(1), 1–24 (1976)

    Article  MathSciNet  Google Scholar 

  14. Phawade, R.: Labelled free choice nets, finite product automata, and expressions. Ph.D. thesis, Homi Bhabha National Institute (2015)

    Google Scholar 

  15. Phawade, R.: Kleene theorems for labelled free choice nets without distributed choice. In: Cabac, L., Kristensen, L.M., Rölke, H. (eds.) Proceedings of PNSE. CEUR Workshop Proceedings, vol. 1591, pp. 132–152. CEUR-WS.org (2016)

    Google Scholar 

  16. Phawade, R.: Kleene theorems free choice nets labelled with distributed alphabets. In: Daniel Moldt, E.K., Rölke, H. (eds.) Proceedings of PNSE. CEUR Workshop Proceedings, vol. 2138, pp. 77–98. CEUR-WS.org (2018)

    Google Scholar 

  17. Phawade, R.: Kleene Theorems for Free Choice Nets Labelled with Distributed Alphabets. arXiv e-prints arXiv:1907.01168, July 2019

  18. Phawade, R., Lodaya, K.: Kleene theorems for labelled free choice nets. In: Moldt, D., Rölke, H. (eds.) Proceedings of PNSE. CEUR Workshop Proceedings, vol. 1160, pp. 75–89. CEUR-WS.org (2014)

    Google Scholar 

  19. Phawade, R., Lodaya, K.: Kleene theorems for synchronous products with matching. In: Koutny, M., Desel, J., Haddad, S. (eds.) Transactions on Petri Nets and Other Models of Concurrency X. LNCS, vol. 9410, pp. 84–108. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48650-4_5

    Chapter  Google Scholar 

  20. Zielonka, W.: Notes on finite asynchronous automata. Inform. Theor. Appl. 21(2), 99–135 (1987)

    Article  MathSciNet  Google Scholar 

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Acknowedgements

We thank anonymous referees of PNSE 2018 workshop and ToPNoC, along with editors Lucio Pomello and Lars Kristensen for their suggestions and patience.

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Authors and Affiliations

  1. Indian Institute of Technology Dharwad, Dharwad, India

    Ramchandra Phawade

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  1. Ramchandra Phawade
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Correspondence to Ramchandra Phawade .

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Editors and Affiliations

  1. Newcastle University, Newcastle upon Tyne, UK

    Maciej Koutny

  2. Università degli Studi di Milano, Milan, Italy

    Lucia Pomello

  3. Western Norway University of Applied Sciences, Bergen, Norway

    Lars Michael Kristensen

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Phawade, R. (2019). Kleene Theorems for Free Choice Automata over Distributed Alphabets. In: Koutny, M., Pomello, L., Kristensen, L. (eds) Transactions on Petri Nets and Other Models of Concurrency XIV. Lecture Notes in Computer Science(), vol 11790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60651-3_6

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  • DOI: https://doi.org/10.1007/978-3-662-60651-3_6

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