Formal Methods in System Design

, Volume 36, Issue 2, pp 167–194 | Cite as

Causal semantics for the algebra of connectors

  • Simon BliudzeEmail author
  • Joseph Sifakis


The Algebra of Connectors \(\mathcal{AC}(P)\) is used to model structured interactions in the BIP component framework. Its terms are connectors, relations describing synchronization constraints between the ports of component-based systems. Connectors are structured combinations of two basic synchronization protocols between ports: rendezvous and broadcast.

In a previous paper, we have studied interaction semantics for \(\mathcal{AC}(P)\) which defines the meaning of connectors as sets of interactions. This semantics reduces broadcasts into the set of their possible interactions and thus blurs the distinction between rendezvous and broadcast. It leads to exponentially complex models that cannot be a basis for efficient implementation. Furthermore, the induced semantic equivalence is not a congruence.

For a subset of \(\mathcal{AC}(P)\), we propose a new causal semantics that does not reduce broadcast into a set of rendezvous and explicitly models the causal dependency relation between ports. The Algebra of Causal Interaction Trees \(\mathcal{T}(P)\) formalizes this subset. It is the set of the terms generated from interactions on the set of ports P, by using two operators: a causality operator and a parallel composition operator. Terms are sets of trees where the successor relation represents causal dependency between interactions: an interaction can participate in a global interaction only if its father participates too. We show that causal semantics is consistent with interaction semantics; the semantic equivalence on \(\mathcal{T}(P)\) is a congruence. Furthermore, it defines an isomorphism between \(\mathcal{T}(P)\) and a subset of \(\mathcal{AC}(P)\).

Finally, we define for causal interaction trees a boolean representation in terms of causal rules. This representation is used for their manipulation and simplification as well as for synthesizing connectors.


BIP Component Connectors Connector synthesis Interaction Causal semantics Causal interaction trees 


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  1. 1.
    Arbab F (2004) Reo: a channel-based coordination model for component composition. Math Struct Comput Sci 14(3):329–366 zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Arbab F, Meng S (2008) Synthesis of connectors from scenario-based interaction specifications. In: CBSE’08. LNCS, vol 5282. Springer, Berlin, pp 114–129 Google Scholar
  3. 3.
    Balarin F, Watanabe Y, Hsieh H, Lavagno L, Passerone C, Sangiovanni-Vincentelli A (2003) Metropolis: an integrated electronic system design environment. IEEE Comput 36(4):45–52 Google Scholar
  4. 4.
    Balasubramanian K, Gokhale A, Karsai G, Sztipanovits J, Neema S (2006) Developing applications using model-driven design environments. IEEE Comput 39(2):33–40 Google Scholar
  5. 5.
    Basu A, Bozga M, Sifakis J (2006) Modeling heterogeneous real-time components in BIP. In: 4th IEEE international conference on software engineering and formal methods (SEFM06), September 2006, pp 3–12. Invited talk Google Scholar
  6. 6.
    Benveniste A, Guernic PL, Jacquemot C (1991) Synchronous programming with events and relations: the SIGNAL language and its semantics. Sci Comput Program 16(2):103–149 zbMATHCrossRefGoogle Scholar
  7. 7.
    Bernardo M, Ciancarini P, Donatiello L (2000) On the formalization of architectural types with process algebras. In: SIGSOFT FSE, pp 140–148 Google Scholar
  8. 8.
  9. 9.
    Bliudze S, Sifakis J (2007) The algebra of connectors—structuring interaction in BIP. In: Proceedings of the EMSOFT’07, pp 11–20. ACM SigBED, October 2007 Google Scholar
  10. 10.
    Bliudze S, Sifakis J (2008) The algebra of connectors—structuring interaction in BIP. IEEE Trans Comput 57(10):1315–1330 CrossRefMathSciNetGoogle Scholar
  11. 11.
    Bliudze S, Sifakis J (2008) A notion of glue expressiveness for component-based systems. In: van Breugel F, Chechik M (eds) CONCUR 2008. LNCS, vol 5201. Springer, Berlin, pp 508–522 CrossRefGoogle Scholar
  12. 12.
    Bruni R, Lanese I, Montanari U (2006) A basic algebra of stateless connectors. Theor Comput Sci 366(1):98–120 zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Darondeau P, Degano P (1989) Causal trees. In: Ausiello G, Dezani-Ciancaglini M, Rocca SRD (eds) ICALP. LNCS, vol 372. Springer, Berlin, pp 234–248 Google Scholar
  14. 14.
    Eker J, Janneck J, Lee E, Liu J, Liu X, Ludvig J, Neuendorffer S, Sachs S, Xiong Y (2003) Taming heterogeneity: the Ptolemy approach. Proc IEEE 91(1):127–144 CrossRefGoogle Scholar
  15. 15.
    Fiadeiro JL (2004) Categories for software engineering. Springer, Berlin Google Scholar
  16. 16.
    Galik O, Bureš T (2005) Generating connectors for heterogeneous deployment. In: SEM’05. ACM, New York, pp 54–61 Google Scholar
  17. 17.
    Halbwachs N, Caspi P, Raymond P, Pilaud D (1991) The synchronous dataflow programming language lustre. Proc IEEE 79:1305–1320 CrossRefGoogle Scholar
  18. 18.
    Hoare CAR (1985) Communicating sequential processes. Prentice Hall international series in computer science. Prentice Hall, New York zbMATHGoogle Scholar
  19. 19.
    Inverardi P, Tivoli M (2001) Automatic synthesis of deadlock free connectors for com/dcom applications. In: ACM proceedings of the joint 8th ESEC and 9th FSE, Vienna, September 2001. ACM, New York Google Scholar
  20. 20.
    Maggiolo-Schettini A, Peron A, Tini S (2003) A comparison of Statecharts step semantics. Theor Comput Sci 290(1):465–498 zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Manna Z, Pnueli A (1992) The temporal logic of reactive and concurrent systems: specification, vol 1. Springer, New York Google Scholar
  22. 22.
    Maraninchi F, Rémond Y (2001) Argos: an automaton-based synchronous language. Comput Lang 27:61–92 zbMATHCrossRefGoogle Scholar
  23. 23.
    Milner R (1989) Communication and concurrency. Prentice Hall international series in computer science. Prentice Hall, New York zbMATHGoogle Scholar
  24. 24.
    Nowak D (2006) Synchronous structures. Inf Comput 204(8):1295–1324 zbMATHCrossRefGoogle Scholar
  25. 25.
    Ray A, Cleaveland R (2003) Architectural interaction diagrams: AIDs for system modeling. In: ICSE’03: proceedings of the 25th international conference on software engineering. IEEE Computer Society, Washington, pp 396–406 CrossRefGoogle Scholar
  26. 26.
    Sifakis J (2005) A framework for component-based construction. In: 3rd IEEE international conference on software engineering and formal methods (SEFM05), September 2005, pp 293–300. Keynote talk Google Scholar
  27. 27.
    Spitznagel B, Garlan D (2003) A compositional formalization of connector wrappers. In: ICSE. IEEE Computer Society, Los Alamitos, pp 374–384 Google Scholar
  28. 28.
    Stefănescu G (2000) Network algebra. Springer, New York zbMATHGoogle Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.CEALISTGif-sur-YvetteFrance
  2. 2.VERIMAGCentre ÉquationGièresFrance

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