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Connector Algebras, Petri Nets, and BIP

  • Roberto Bruni
  • Hernán Melgratti
  • Ugo Montanari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7162)

Abstract

In the area of component-based software architectures, the term connector has been coined to denote an entity (e.g. the communication network, middleware or infrastructure) that regulates the interaction of independent components. Hence, a rigorous mathematical foundation for connectors is crucial for the study of coordinated systems. In recent years, many different mathematical frameworks have been proposed to specify, design, analyse, compare, prototype and implement connectors rigorously. In this paper, we overview the main features of three notable frameworks and discuss their similarities, differences, mutual embedding and possible enhancements. First, we show that Sobocinski’s nets with boundaries are as expressive as Sifakis et al.’s BI(P), the BIP component framework without priorities. Second, we provide a basic algebra of connectors for BI(P) by exploiting Montanari et al.’s tile model and a recent correspondence result with nets with boundaries. Finally, we exploit the tile model as a unifying framework to compare BI(P) with other models of connectors and to propose suitable enhancements of BI(P).

Keywords

Transition System Monoidal Category Sequential Composition Parallel Composition Label Transition System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Arbab, F.: Reo: a channel-based coordination model for component composition. Mathematical Structures in Computer Science 14(3), 329–366 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Arbab, F., Bruni, R., Clarke, D., Lanese, I., Montanari, U.: Tiles for Reo. In: Corradini, A., Montanari, U. (eds.) WADT 2008. LNCS, vol. 5486, pp. 37–55. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Arbab, F., Rutten, J.J.M.M.: A Coinductive Calculus of Component Connectors. In: Wirsing, M., Pattinson, D., Hennicker, R. (eds.) WADT 2003. LNCS, vol. 2755, pp. 34–55. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Baier, C., Sirjani, M., Arbab, F., Rutten, J.J.M.M.: Modeling component connectors in Reo by constraint automata. Sci. Comput. Program 61(2), 75–113 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Baldan, P., Corradini, A., Ehrig, H., Heckel, R.: Compositional semantics for open Petri nets based on deterministic processes. Mathematical Structures in Computer Science 15(1), 1–35 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Basu, A., Bozga, M., Sifakis, J.: Modeling heterogeneous real-time components in BIP. In: Fourth IEEE International Conference on Software Engineering and Formal Methods (SEFM 2006), pp. 3–12. IEEE Computer Society (2006)Google Scholar
  7. 7.
    Bliudze, S., Sifakis, J.: The algebra of connectors - structuring interaction in BIP. IEEE Trans. Computers 57(10), 1315–1330 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bliudze, S., Sifakis, J.: Causal semantics for the algebra of connectors. Formal Methods in System Design 36(2), 167–194 (2010)zbMATHCrossRefGoogle Scholar
  9. 9.
    Bruni, R.: Tile Logic for Synchronized Rewriting of Concurrent Systems. PhD thesis, Computer Science Department, University of Pisa, Published as Technical Report TD-1/99 (1999)Google Scholar
  10. 10.
    Bruni, R., Gadducci, F., Montanari, U.: Normal forms for algebras of connection. Theor. Comput. Sci. 286(2), 247–292 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Bruni, R., Lanese, I., Montanari, U.: A basic algebra of stateless connectors. Theor. Comput. Sci. 366(1-2), 98–120 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Bruni, R., Melgratti, H., Montanari, U.: A Connector Algebra for P/T Nets Interactions. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011 – Concurrency Theory. LNCS, vol. 6901, pp. 312–326. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Bruni, R., Meseguer, J., Montanari, U.: Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science 12(1), 53–90 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Bruni, R., Montanari, U.: Cartesian closed double categories, their lambda-notation, and the pi-calculus. In: LICS, pp. 246–265 (1999)Google Scholar
  15. 15.
    Bruni, R., Montanari, U.: Dynamic connectors for concurrency. Theor. Comput. Sci. 281(1-2), 131–176 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Bruni, R., Montanari, U., Rossi, F.: An interactive semantics of logic programming. TPLP 1(6), 647–690 (2001)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Clarke, D., Costa, D., Arbab, F.: Connector colouring I: Synchronisation and context dependency. Sci. Comput. Program 66(3), 205–225 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Ferrari, G.L., Montanari, U.: Tile formats for located and mobile systems. Inf. Comput. 156(1-2), 173–235 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Fiadeiro, J.L., Maibaum, T.S.E.: Categorical semantics of parallel program design. Sci. Comput. Program 28(2-3), 111–138 (1997)zbMATHCrossRefGoogle Scholar
  20. 20.
    Gadducci, F., Montanari, U.: The tile model. In: Plotkin, G.D., Stirling, C., Tofte, M. (eds.) Proof, Language, and Interaction, pp. 133–166. The MIT Press (2000)Google Scholar
  21. 21.
    Gadducci, F., Montanari, U.: Comparing logics for rewriting: rewriting logic, action calculi and tile logic. Theor. Comput. Sci. 285(2), 319–358 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Katis, P., Sabadini, N., Walters, R.F.C.: Representing Place/Transition Nets in Span(Graph). In: Johnson, M. (ed.) AMAST 1997. LNCS, vol. 1349, pp. 322–336. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  23. 23.
    Katis, P., Sabadini, N., Walters, R.F.C.: Span(Graph): A Categorial Algebra of Transition Systems. In: Johnson, M. (ed.) AMAST 1997. LNCS, vol. 1349, pp. 307–321. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  24. 24.
    König, B., Montanari, U.: Observational Equivalence for Synchronized Graph Rewriting with Mobility. In: Kobayashi, N., Babu, C. S. (eds.) TACS 2001. LNCS, vol. 2215, pp. 145–164. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  25. 25.
    MacLane, S.: Categories for the Working Mathematician, 2nd edn. Springer, Heidelberg (1998)Google Scholar
  26. 26.
    Montanari, U., Rossi, F.: Graph rewriting, constraint solving and tiles for coordinating distributed systems. Applied Categorical Structures 7(4), 333–370 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Perry, D.E., Wolf, E.L.: Foundations for the study of software architecture. ACM SIGSOFT Software Engineering Notes 17, 40–52 (1992)CrossRefGoogle Scholar
  28. 28.
    Petri, C.: Kommunikation mit Automaten. PhD thesis, Institut für Instrumentelle Mathematik, Bonn (1962)Google Scholar
  29. 29.
    Sobocinski, P.: A non-interleaving process calculus for multi-party synchronisation. In: Bonchi, F., Grohmann, D., Spoletini, P., Tuosto, E. (eds.) ICE. EPTCS, vol. 12, pp. 87–98 (2009)Google Scholar
  30. 30.
    Sobociński, P.: Representations of Petri Net Interactions. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 554–568. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  31. 31.
    Stefanescu, G.: Reaction and control I. mixing additive and multiplicative network algebras. Logic Journal of the IGPL 6(2), 348–369 (1998)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Roberto Bruni
    • 1
  • Hernán Melgratti
    • 2
  • Ugo Montanari
    • 1
  1. 1.Dipartimento di InformaticaUniversità di PisaItaly
  2. 2.Departamento de ComputaciónUniversidad de Buenos Aires - ConicetArgentina

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