An Introduction to the π-Calculus

@inproceedings{Parrow2001AnIT,
  title={An Introduction to the $\pi$-Calculus},
  author={Joachim Parrow},
  booktitle={Handbook of Process Algebra},
  year={2001}
}
  • J. Parrow
  • Published in Handbook of Process Algebra 2001
  • Computer Science
Context-based process algebras for mobility
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Two new formalisations of the finite fragment of the /spl pi/-calculus are provided, defined in a way which exhibits the global state and the execution context of a process without needing to rely heavily on term rewriting techniques.
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TLDR
This construction renders in a compositional way the control flow aspects present in π-calculus process expressions, by adapting the existing graph-theoretic net composition operators.
Expressiveness of the π-Calculus and the $-Calculus
TLDR
It is demonstrated that both models are more expressive than Turing Machines, i.e., they belong to superTuring models of computation, and are able to solve the halting problem of the Universal Turing Machine.
Free-Algebra Models for the pi-Calculus
TLDR
A novel algebraic description for models of the @p-calculus is obtained, and an existing construction is validated as the universal such model, and it is generalised to prove that all free-algebra models are fully abstract.
Open Bisimulation, Revisited
Free-algebra models for the pi -calculus
  • I. Stark
  • Mathematics
    Theor. Comput. Sci.
  • 2008
Controlling Process Modularity in Mobile Computing
TLDR
A variant of π-calculus which can flexibly and dynamically control process modularity is presented, and a notion of bisimulation-preorder is proposed to reflect some aspects of mobile distributed computing such as interaction costs.
A Hierarchy of Behavioral Equivalences in the π-calculus with Noisy Channels
TLDR
An early transitional semantics of the ρN-calculus is presented, which is not a directly translated version of the late semantics of πN, and six kinds of behavioral equivalences are extended, which are helpful to verify behavioral equivalence of two agents.
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References

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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.
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Two semantics for a parallel object-oriented programming language are presented. One is a two-level transitional semantics in which the global behaviour of a system is derived directly from the
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The Weak Late π-calculus semantics can be characterized as ordinary Observation congruence over a specialized transition system where both the instantiation of input placeholders and the name substitutions are explicitly handled via suitable constructors.
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This paper exhibits accurate encodings of the λ-calculus in the π-calculus. The former is canonical for calculation with functions, while the latter is a recent step [15] towards a canonical
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TLDR
This work introduces a calculus for concurrent and communicating processes, which is a direct and simple extension of the λ-calculus, and shows that the ε-abstraction is a particular case of reception (on a port named λ), and application is a specific case of cooperation.
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