@Article{BliSif10-causal-fmsd,
  author = 	 {Simon Bliudze and Joseph Sifakis},
  title = 	 {Causal semantics for the algebra of connectors},
  journal = 	 {Formal Methods in System Design},
  year = 	 2010,
  volume = 	 36,
  number = 	 2,
  pages = 	 {167--194},
  month = 	 jun,
  publisher =    {Springer},
  doi =          {10.1007/s10703-010-0091-z}
}

@InProceedings{BliSif08-causal-fmco,
  author = 	 {Simon Bliudze and Joseph Sifakis},
  title = 	 {Causal Semantics for the Algebra of Connectors 
                  (Extended abstract)},
  booktitle =	 {FMCO 2007},
  year =	 2008,
  editor =	 {Frank de Boer and Marcello Bonsangue},
  series =	 {LNCS},
  number =       5382,
  pages =        {179--199},
  publisher =    {Springer-Verlag},
  address =      {Berlin Heidelberg},
  doi =          {10.1007/978-3-540-92188-2_8}
}

@TechReport{BliSif08-causal-tr,
  author = {Simon Bliudze and Joseph Sifakis},
  title = {Causal Semantics for the Algebra of Connectors},
  institution = {Verimag},
  year = 2008,
  month = mar,
  number = {TR-2008-4},
  address = {Centre \'Equation, 38610 Gi\`eres},
  url = {http://www-verimag.imag.fr/index.php?page=techrep-list}
  abstract = {
    The Algebra of Connectors $\ac(P)$ is used to model structured
    interactions in the BIP component framework.  Its terms are
    \emph{connectors}, relations describing synchronization constraints
    between the ports of component-based systems.  Connectors are 
    structured combinations of two basic synchronization protocols 
    between ports: \emph{rendezvous} and \emph{broadcast}.
  
    In a previous paper, we have studied interaction semantics for $\ac(P)$
    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 $\ac(P)$, we propose a new \emph{causal} semantics that
    does not reduce broadcast into a set of rendezvous and explicitly models
    the causal dependency relation between triggers and synchrons.  The
    Algebra of Causal Trees $\ct(P)$ formalizes this subset.  It is the set
    of the terms generated from interactions on the set of ports $P$, by
    using two operators: a \emph{causality} operator and a \emph{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.  Furthermore, it defines an isomorphism between
    $\ct(P)$ and the set of the terms of $\ac(P)$ involving triggers.
 
    Finally, we define for causal trees a boolean representation in terms of
    \emph{causal rules}.  This representation is used for their manipulation
    and simplification as well as for synthesizing connectors.
  }
}