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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A preliminary version of this paper appeared at 14th PNSE workshop, held at Bratislava [16].
References
Antimirov, V.: Partial derivatives of regular expressions and finite automaton constructions. Theoret. Comput. Sci. 155(2), 291–319 (1996)
Brzozowski, J.A.: Derivatives of regular expressions. J. ACM 11(4), 481–494 (1964)
Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge University Press, New York (1995)
Garg, V.K., Ragunath, M.: Concurrent regular expressions and their relationship to petri nets. Theoret. Comput. Sci. 96(2), 285–304 (1992)
Grabowski, J.: On partial languages. Fundam. Inform. 4(2), 427–498 (1981)
Hack, M.H.T.: Analysis of production schemata by Petri nets. Project Mac Report TR-94, MIT (1972)
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)
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
Lodaya, K.: Product automata and process algebra. In: SEFM. IEEE (2006)
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
Mirkin, B.G.: An algorithm for constructing a base in a language of regular expressions. Eng. Cybern. 5, 110–116 (1966)
Mukund, M.: Automata on distributed alphabets. In: D’Souza, D., Shankar, P. (eds.) Modern Applications of Automata Theory. World Scientific (2011)
Petersen, J.L.: Computation sequence sets. J. Comput. Syst. Sci. 13(1), 1–24 (1976)
Phawade, R.: Labelled free choice nets, finite product automata, and expressions. Ph.D. thesis, Homi Bhabha National Institute (2015)
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)
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)
Phawade, R.: Kleene Theorems for Free Choice Nets Labelled with Distributed Alphabets. arXiv e-prints arXiv:1907.01168, July 2019
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)
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
Zielonka, W.: Notes on finite asynchronous automata. Inform. Theor. Appl. 21(2), 99–135 (1987)
Acknowedgements
We thank anonymous referees of PNSE 2018 workshop and ToPNoC, along with editors Lucio Pomello and Lars Kristensen for their suggestions and patience.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer-Verlag GmbH Germany, part of Springer Nature
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-662-60651-3_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-60650-6
Online ISBN: 978-3-662-60651-3
eBook Packages: Computer ScienceComputer Science (R0)