Abstract
We propose a method for reducing a partially ordered set, in such a way that the lattice derived from a closure operator based on concurrency is changed as little as possible. In fact, we characterize in which cases it remains unchanged, and prove minimality of the resulting reduced poset. In these cases, we can complete this poset so as to obtain a causal net on which the closure operator will lead to the same lattice.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bernardinello, L., Ferigato, C., Haar, S., Pomello, L.: Closed sets in occurrence nets with conflicts. Fund. Inform. 133(4), 323–344 (2014)
Bernardinello, L., Pomello, L., Rombolà, S.: Closure operators and lattices derived from concurrency in posets and occurrence nets. Fund. Inform. 105, 211–235 (2010)
Bernardinello, L., Pomello, L., Rombolà, S.: Orthomodular algebraic lattices related to combinatorial posets. In: Proceedings of the 15th Italian Conference on Theoretical Computer Science, Perugia, Italy, 17–19 September 2014, pp. 241–245 (2014)
Best, E., Fernandez, C.: Nonsequential Processes-A Petri Net View. Monographs in Theoretical Computer Science. An EATCS Series, vol. 13. Springer, Heidelberg (1988)
Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society, Providence (1979)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)
Dushnik, B., Miller, E.W.: Partially ordered sets. Am. J. Math. 63(3), 600–610 (1941)
Kalmbach, G.: Orthomodular Lattices. Academic Press, New York (1983)
Mazurkiewicz, A.: Trace theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) ACPN 1986. LNCS, vol. 255, pp. 278–324. Springer, Heidelberg (1987). doi:10.1007/3-540-17906-2_30
Möhring, R.H.: Algorithmic aspects of comparability graphs, interval graphs. In: Rival, I. (ed.) Graphs, Order: The Role of Graphs in the Theory of Ordered Sets and Its Applications, pp. 41–101. Springer Netherlands, Dordrecht (1985)
Nielsen, M., Plotkin, G.D., Winskel, G.: Petri nets, event structures and domains, part I. Theor. Comput. Sci. 13, 85–108 (1981)
Petri, C.A., Smith, E.: Concurrency and continuity. In: Rozenberg, G. (ed.) APN 1986. LNCS, vol. 266, pp. 273–292. Springer, Heidelberg (1987). doi:10.1007/3-540-18086-9_30
Smith, E.: Carl Adam Petri: Life and Science. Springer, Heidelberg (2015)
Winskel, G.: Event structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) ACPN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987). doi:10.1007/3-540-17906-2_31
Acknowledgments
Work partially supported by MIUR.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Puerto, A. (2017). Concurrency-Preserving Minimal Process Representation. In: Höfner, P., Pous, D., Struth, G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2017. Lecture Notes in Computer Science(), vol 10226. Springer, Cham. https://doi.org/10.1007/978-3-319-57418-9_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-57418-9_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-57417-2
Online ISBN: 978-3-319-57418-9
eBook Packages: Computer ScienceComputer Science (R0)