Solo Diagrams

@inproceedings{Laneve2001SoloD,
  title={Solo Diagrams},
  author={Cosimo Laneve and Joachim Parrow and Bj{\"o}rn Victor},
  booktitle={TACS},
  year={2001}
}
We address the problems of implementing the replication operator efficiently in the solos calculus - a calculus of mobile processes without prefix. This calculus is expressive enough to admit an encoding of the whole fusion calculus and thus the ?-calculus. We show that nested occurrences of replication can be avoided, that the size of replicated terms can be limited to three particles, and that the usual unfolding semantics of replication can be replaced by three simple reduction rules. To… 
Solos in Concert
TLDR
Using two different encodings, it is shown that the solos calculus can express both action prefix and guarded summation, and the expressive power of thesolos calculus is still retained by the sub-calculus where actions carry at most two names.
Acyclic Solos and Differential Interaction Nets
TLDR
A restriction of the solos calculus is presented which is stable under reduction and expressive enough to contain an encoding of the pi-calculus, and it is shown that equalizing names that are already equal is not required by the encoding of this calculus.
Concurrent Nets: A Study of Prefixing in Process Calculi
On differential interaction nets and the pi-calculus
TLDR
This work proves that the nets obtained by this translation of a finitary version of the pi-calculus satisfy an acyclicity criterion weaker than the standard Girard (or Danos-Regnier) acyClicity criterion, and provides a Curry-Howard interpretation of processes.
Term Graph Rewriting for the pi-Calculus
TLDR
A graphical implementation for (possibly) recursive processes of the π-calculus, encoding each process into a term graph, which allows for using standard graph rewriting mechanisms in modelling the reduction semantics of the calculus.
Graph rewriting for the π-calculus†
  • F. Gadducci
  • Mathematics, Computer Science
    Mathematical Structures in Computer Science
  • 2007
TLDR
A graphical implementation for (possibly recursive) processes of the π-calculus, encoding each process into a graph, which allows the use of standard graph rewriting mechanisms for modelling the reduction semantics of the calculus.
Proof Nets in Process Algebraic Form
We present δ-calculus, a computational interpretation of Linear Logic, in the form of a typed process algebra whose structures correspond to Proof Nets, and where typing derivations correspond to
Explicit fusions
The true concurrency of differential interaction nets
  • Damiano Mazza
  • Computer Science
    Mathematical Structures in Computer Science
  • 2016
TLDR
It is inferred that no reasonably expressive process calculus may be satisfactorily encoded in differential interaction nets, and an analysis of one such encoding proposed by Ehrhard and Laurent is argued that it does not contradict the claims, but rather supports them.
...
...

References

SHOWING 1-10 OF 30 REFERENCES
Solos in Concert
TLDR
Using two different encodings, it is shown that the solos calculus can express both action prefix and guarded summation, and the expressive power of thesolos calculus is still retained by the sub-calculus where actions carry at most two names.
The fusion calculus: expressiveness and symmetry in mobile processes
  • J. Parrow, B. Victor
  • Computer Science
    Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)
  • 1998
TLDR
The fusion calculus contains the polyadic /spl pi/-calculus as a proper subcalculus and thus inherits all its expressive power, and is presented as a significant step towards a canonical calculus of concurrency.
The reflexive CHAM and the join-calculus
By adding reflexion to the chemical machine of Berry and Boudol, we obtain a formal model of concurrency that is consistent with mobility and distribution. Our model provides the foundations of a
The Polyadic π-Calculus: a Tutorial
TLDR
The π-calculus is a model of concurrent computation based upon the notion of naming that is generalized from monadic to polyadic form and semantics is done in terms of both a reduction system and a version of labelled transitions called commitment.
A Calculus of Mobile Processes, Part I
TLDR
The paper continues by presenting the algebraic theory of strong bisimilarity and strong equivalence, including a new notion of equivalence indexed by distinctions, based upon a semantics in terms of a labelled transition system and a notion of weak bisimulation, both of which are expounded in detail in a companion paper.
Graph Notation for Concurrent Combinators
  • N. Yoshida
  • Computer Science, Mathematics
    Theory and Practice of Parallel Programming
  • 1994
TLDR
This work introduces graph notation for concurrent processes which does not use the notion of port names for its formulation, and shows how basic elements of process calculi such as agents, reduction, and behavioural equivalences are soundly formulated in the new setting.
Asynchrony and the -calculus (note)
TLDR
It is shown that this simple message passing discipline, together with the restriction construct making a name private for an agent, is enough to encode the synchronous communication of the Milner's-calculus.
On the pi-Calculus and Linear Logic
An Object Calculus for Asynchronous Communication
TLDR
This paper shows basic construction of the formal system along with several illustrative examples of the communication primitive, which results in a consistent reduction of Milner's calculus, while retaining the same expressive power.
...
...