Abstract
Graph grammars are a powerful model of concurrent and distributed systems which can be seen as a proper extension of Petri nets. Inspired by this correspondence, a truly concurrent semantics has been developed along the years for the algebraic approaches to graph grammars, based on Winskel’s style unfolding constructions as well as on suitable notions of processes. A basic role is played in this framework by the study of contextual and inhibitor nets, two extensions of ordinary nets which can be seen as intermediate models between ordinary Petri nets and algebraic graph grammars.
This paper presents a survey of these results, discussing in a precise, even if informal way, some of the main technical contributions that made possible the development of such a theory.
Research partially supported by the EU FET-GC Project IST-2001-32747 agile, and by the EC RTN 2-2001-00346 SegraVis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agerwala, T., Flynn, M.: Comments on capabilities, limitations and “correctness” of Petri nets. Computer Architecture News 4(2), 81–86 (1973)
Baldan, P.: Modelling concurrent computations: from contextual Petri nets to graph grammars. PhD thesis, Department of Computer Science, University of Pisa (2000), Available as technical report n. TD-1/00
Baldan, P., Busi, N., Corradini, A., Pinna, G.M.: Domain and event structure semantics for Petri nets with read and inhibitor arcs. Theoretical Computer Science (2004) (to appear)
Baldan, P., Busi, N., Corradini, A., Pinna, G.M.: Functional concurrent semantics for petri nets with read and inhibitor arcs. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 442–457. Springer, Heidelberg (2000)
Baldan, P., Corradini, A., König, B.: A static analysis technique for graph transformation systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 381–395. Springer, Heidelberg (2001)
Baldan, P., Corradini, A., König, B.: Verifying finite-state graph grammars: An unfolding-based approach. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 83–98. Springer, Heidelberg (2004)
Baldan, P., Corradini, A., Montanari, U.: Contextual Petri nets, asymmetric event structures and processes. Information and Computation 171(1), 1–49 (2001)
Baldan, P., Corradini, A., Montanari, U.: Concatenable graph processes: Relating processes and derivation traces. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 283–295. Springer, Heidelberg (1998)
Baldan, P., Corradini, A., Montanari, U.: Unfolding and event structure semantics for graph grammars. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578, pp. 73–89. Springer, Heidelberg (1999)
Baldan, P., Corradini, A., Montanari, U.: Unfolding of double-pushout graph grammars is a coreflection. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) TAGT 1998. LNCS, vol. 1764, pp. 145–163. Springer, Heidelberg (2000)
Baldan, P., Corradini, A., Montanari, U.: Bisimulation equivalences for graph grammars. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, vol. 2300, pp. 158–190. Springer, Heidelberg (2002)
Baldan, P., Corradini, A., Montanari, U., Ribeiro, L.: Coreflective concurrent semantics for single-pushout graph grammars. In: Wirsing, M., Pattinson, D., Hennicker, R. (eds.) WADT 2003. LNCS, vol. 2755, pp. 165–184. Springer, Heidelberg (2003)
Baldan, P., König, B.: Approximating the behaviour of graph transformation systems. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 14–30. Springer, Heidelberg (2002)
Bueno, F., Hermenegildo, M., Montanari, U., Rossi, F.: Partial order and contextual net semantics for atomic and locally atomic CC programs. Science of Computer Programming 30, 51–82 (1998)
Busi, N.: Petri Nets with Inhibitor and Read Arcs: Semantics, Analysis and Application to Process Calculi. PhD thesis, University of Siena, Department of Computer Science (1998)
Christensen, S., Hansen, N.D.: Coloured Petri nets extended with place capacities, test arcs and inhibitor arcs. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 186–205. Springer, Heidelberg (1993)
Corradini, A.: Concurrent graph and term graph rewriting. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 438–464. Springer, Heidelberg (1996)
Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F.: Abstract graph derivations in the double-pushout approach. In: Ehrig, H., Schneider, H.-J. (eds.) Dagstuhl Seminar 1993. LNCS, vol. 776, pp. 86–103. Springer, Heidelberg (1994)
Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F.: An event structure semantics for safe graph grammars. In: Olderog, E.-R. (ed.) Programming Concepts, Methods and Calculi. IFIP Transactions, vol. A-56, pp. 423–444. North-Holland, Amsterdam (1994)
Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F.: An event structure semantics for graph grammars with parallel productions. In: Cuny, J., Engels, G., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1994. LNCS, vol. 1073, Springer, Heidelberg (1996)
Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fundamenta Informaticae 26, 241–265 (1996)
Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic Approaches to Graph Transformation I: Basic Concepts and Double Pushout Approach. In: Rozenberg [45], ch. 3
De Francesco, N., Montanari, U., Ristori, G.: Modeling Concurrent Accesses to Shared Data via Petri Nets. In: Programming Concepts, Methods and Calculi, IFIP Transactions, vol. A-56, pp. 403–422. North Holland, Amsterdam (1994)
Degano, P., Meseguer, J., Montanari, U.: Axiomatizing the algebra of net computations and processes. Acta Informatica 33, 641–647 (1996)
Ehrig, H.: Tutorial introduction to the algebraic approach of graph-grammars. In: Ehrig, H., Nagl, M., Rosenfeld, A., Rozenberg, G. (eds.) Graph Grammars 1986. LNCS, vol. 291, pp. 3–14. Springer, Heidelberg (1987)
Ehrig, H., Habel, A., Kreowski, H.-J., Parisi-Presicce, F.: Parallelism and concurrency in High-Level Replacement Systems. Mathematical Structures in Computer Science 1, 361–404 (1991)
Ehrig, H., Heckel, R., Korff, M., L”owe, M., Ribeiro, L., Wagner, A., Corradini, A.: Algebraic approaches to graph transformation II: Single pushout approach and comparison with double pushout approach. In: Rozenberg [45], ch. 4
Golz, U., Reisig, W.: The non-sequential behaviour of Petri nets. Information and Control 57, 125–147 (1983)
Janicki, R., Koutny, M.: Invariant semantics of nets with inhibitor arcs. In: Groote, J.F., Baeten, J.C.M. (eds.) CONCUR 1991. LNCS, vol. 527. Springer, Heidelberg (1991)
Janicki, R., Koutny, M.: Semantics of inhibitor nets. Information and Computation 123, 1–16 (1995)
Kreowski, H.-J.: Manipulation von Graphmanipulationen. PhD thesis, Technische Universität Berlin (1977)
Lack, S., Sobociński, P.: Adhesive categories. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 273–288. Springer, Heidelberg (2004)
Löwe, M.: Algebraic approach to single-pushout graph transformation. Theoretical Computer Science 109, 181–224 (1993)
McMillan, K.L.: Symbolic Model Checking. Kluwer, Dordrecht (1993)
Meseguer, J., Montanari, U., Sassone, V.: Process versus unfolding semantics for Place/Transition Petri nets. Theoretical Computer Science 153(1-2), 171–210 (1996)
Meseguer, J., Montanari, U., Sassone, V.: On the semantics of Place/Transition Petri nets. Mathematical Structures in Computer Science 7, 359–397 (1997)
Montanari, U., Rossi, F.: Contextual nets. Acta Informatica 32(6) (1995)
Nielsen, M., Plotkin, G., Winskel, G.: Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85–108 (1981)
Peterson, J.L.: Petri Net Theory and the Modelling of Systems. Prentice-Hall, Englewood Cliffs (1981)
Petri, C.A.: Kommunikation mit Automaten. PhD thesis, Schriften des Institutes für Instrumentelle Matematik, Bonn (1962)
Petri, C.A.: Non-sequential processes. Technical Report GMD-ISF-77-5, Gesellshaft für Mathematik und Datenverarbeitung, Bonn (1977)
Reisig, W.: Petri Nets: An Introduction. In: EACTS Monographs on Theoretical Computer Science. Springer, Heidelberg (1985)
Ribeiro, L.: Parallel Composition and Unfolding Semantics of Graph Grammars. PhD thesis, Technische Universität Berlin (1996)
Ristori, G.: Modelling Systems with Shared Resources via Petri Nets. PhD thesis, Department of Computer Science - University of Pisa (1994)
Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1. World Scientific, Foundations (1997)
Schied, G.: On relating rewriting systems and graph grammars to event structures. In: Ehrig, H., Schneider, H.-J. (eds.) Dagstuhl Seminar 1993. LNCS, vol. 776, pp. 326–340. Springer, Heidelberg (1994)
Scott, D.S.: Outline of a mathematical theory of computation. In: Proceedings of the Fourth Annual Princeton Conference on Information Sciences and Systems, pp. 169–176 (1970)
van Glabbeek, R., Goltz, U.: Equivalence notions for concurrent systems and refinement of actions. In: Kreczmar, A., Mirkowska, G. (eds.) Proceedings of MFCS 1989. LNCS, vol. 39, pp. 237–248. Springer, Heidelberg (1989)
Vogler, W.: Efficiency of asynchronous systems and read arcs in Petri nets. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 538–548. Springer, Heidelberg (1997)
Vogler, W., Semenov, A., Yakovlev, A.: Unfolding and finite prefix for nets with read arcs. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 501–516. Springer, Heidelberg (1998)
Winskel, G.: Event Structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Baldan, P., Corradini, A. (2005). On the Concurrent Semantics of Algebraic Graph Grammars. In: Kreowski, HJ., Montanari, U., Orejas, F., Rozenberg, G., Taentzer, G. (eds) Formal Methods in Software and Systems Modeling. Lecture Notes in Computer Science, vol 3393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31847-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-31847-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24936-8
Online ISBN: 978-3-540-31847-7
eBook Packages: Computer ScienceComputer Science (R0)