Loose semantics of petri nets
January 2005
Pages 370 - 384
Abstract
In this paper, we propose a new,loose semantics for place/tran- sition nets based on transition systems and generalizing the reachability graph semantics. The loose semantics of a place/transition net reflects all its possible refinements and is given as a category of transition systems with alternative sequences of events over the net. The main result states that each plain morphism between two place/transitions nets induces a free construction between the corresponding semantic categories.
References
[1]
L. Bernadinello and F. De Cindio. A survey of basic net models and modular net classes. Advances in Petri Nets 1992, LNCS 609,pp: 304-351, Springer, 1992.
[2]
E. Best and J. Desel. Partial order behaviour and structure of Petri nets. Formal Aspects of Computing, pages 123-138, 1990.
[3]
A. Corradini, H. Ehrig, M. Löwe, U. Montanari, and F. Rossi. An event structure semantics for safe graph grammars. In Proc. PROCOMET'94, IFIP TC2 Working Conf., San Miniato 1994, pages 417-439. IFIP TCS, 1994.
[4]
S. Christensen and L. Petrucci. Modular analysis of Petri nets. Computer Journal, 43(3):224-242, 2000.
[5]
J. Desel, G. Juhás, and R. Lorenz. Petri Nets over Partial Algebras. In H. Ehrig, G. Juhás, J. Padberg, and G. Rozenberg, editors, Advances in Petri Nets: Unifying Petri Nets, volume 2128 of LNCS. Springer, 2001.
[6]
J. Desel and W. Reisig. Place/transition Petri nets. InW. Reisig and G. Rozenberg, editors, Lectures on Petri Nets: Basic Models, pages 122-173. Springer Verlag, LNCS 1491, 1998.
[7]
H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 2: Module Specifications and Constraints, volume 21 of EATCS Monographs on Theoretical Computer Science. Springer Verlag, Berlin, 1990.
[8]
H. Ehrig, F. Orejas, B. Braatz, M. Klein, and M. Piirainen. A Generic Component Concept for System Modelling. In R. Kutsche, H. Weber (Eds.) Proc. FASE 2002: Formal Aspects of Software Engineering, LNCS 2306, pages 33-48. Springer, 2002.
[9]
P. Huber, K. Jensen, and R.M. Shapiro. Hierarchies in Coloured Petri Nets. In G. Rozenberg, editor, Advances in Petri nets 1990, LNCS 483, pages 313-341. Springer, 1991.
[10]
P. W. Hoogers, H. C. M. Kleijn, and P. S. Thiagarajan. A trace semantics for Petri nets. Information and Computation, 117(1):98-114, 1995.
[11]
G. Juhás and R. Lorenz. Modelling with Petri modules. In B. Caillaud, X. Xie, and L. Darondeau, Ph.and Lavagno, editors, Synthesis and Control of Discrete Event Systems, pages 125-138. Kluwer Academic Publishers, 2002.
[12]
E. Kindler. A compositional partial order semantics for petri net components. In Azéma, P. and Balbo, G., editors, 18th Int. Conf. on Application and Theory of Petri Nets, LNCS 1248, pages 235-252. Springer-Verlag, 1997.
[13]
A. Mazurkiewicz. Basic notions of trace theory. In de Bakker, J.W. et al., editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency., LNCS 354, pages 285-363. Springer, 1989.
[14]
J. Meseguer and U. Montanari. Petri Nets are Monoids. Information and Computation, 88(2):105-155, 1990.
[15]
R. Morin and B. Rozoy. On the semantics of place/transition nets. In CONCUR 99, LNCS 1664, pages 447-462. Springer, 1999.
[16]
H. Müller and H. Weber, editors. Continuous Engineering of Industrial Scale Software Systems. IBFI, Schloß Dagstuhl, Dagstuhl Seminar Report #98092, 1998.
[17]
M. Nielsen, G. Plotkin, and G.Winskel. Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science, 13:85-108, 1981.
[18]
M. Nielsen and V. Sassone. Petri nets and other models of concurrency. In W. Reisig and G. Rozenberg, editors, Lectures on Petri Nets I: Basic Models, LNCS 1491, pages 587-642. Springer, 1998.
[19]
M. Nielsen, V. Sassone, and G. Winskel. Relationships Beween Models of Concurrency . In G. Rozenberg, J.W. de Bakker, W.-P. de Roever, editors, A Decade of Concurrency, pages 425 - 476. LNCS 803, 1993.
[20]
J. Padberg. Petri net modules. Journal on Integrated Design and Process Technology, 6(4):105-120, 2002.
[21]
J. Padberg. Transition systems with alternatives: an approach to a loose semantics of place/transition nets. Technical Report 2003-18, Technical University Berlin, 2003.
[22]
J. Padberg and H. Ehrig. Petri net modules in the transformation-based component framework. Journal of Logic and Algebraic Programming, 2003. submitted.
[23]
W. Reisig. Petri Nets, volume 4 of EATCS Monographs on Theoretical Computer Science. Springer Verlag, 1985.
[24]
H. Reichel. Specification semantics. In E. Astesiano, H.-J. Kreowski, and B. Krieg-Brückner, editors, Algebraic Foundations of System Specification, IFIP State-of-the-Art Reports, chapter 5, pages 131-158. Springer Verlag, 1999.
[25]
B. Rozoy. On distributed languages and models for concurrency. In G. Rozenberg, editor, Advances in Petri Nets, LNCS 609, pages 267-291. Springer, 1992.
[26]
H. Weber. Continuous Engineering of Communication and Software Infrastructures. In J.P. Finance (ed); Fundamental Approaches to Software Engineering (FASE'99), LNCS 1577, 1999, pages 22-29. Springer Verlag, Berlin, Heidelberg, New York, 1999.
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January 2005
404 pages
ISBN:3540249362
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Springer-Verlag
Berlin, Heidelberg
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Published: 01 January 2005
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