An Introduction to the π-Calculus

  title={An Introduction to the $\pi$-Calculus},
  author={Joachim Parrow},
  booktitle={Handbook of Process Algebra},
  • J. Parrow
  • Published in Handbook of Process Algebra 2001
  • Computer Science
Context-based process algebras for mobility
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.
Introduction to Concurrency Theory
This introductory chapter outlines the main motivations for the study of concurrency theory and the differences with respect to the theory of sequential computation. It also reports the structure of
Petri Net Semantics of the Finite pi-calculus Terms
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
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
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
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
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.


The Polyadic π-Calculus: a Tutorial
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.
Objects in the pi-Calculus
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
An Object Calculus for Asynchronous Communication
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.
A Symbolic Semantics for the pi-Calculus
A sound and complete proof system is introduced for symbolic bisimulation, which is more amenable to automatic manipulation and sheds light on the logical differences among different forms of bisimulations over algebras of name-passing processes.
On Encoding p-pi in m-pi
A type system for mπ processes is introduced which captures the interaction regime underlying the encoding of pπ processes respecting a sorting, and a full-abstraction result is shown: two p π processes are typed barbed congruent iff their mπ encodings are monadic-typed barbedCongruent.
The Weak Late pi-Calculus Semantics as Observation Equivalence
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.
Functions as Processes
  • R. Milner
  • Computer Science, Mathematics
    Math. Struct. Comput. Sci.
  • 1992
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
A Calculus of Communicating Systems
  • R. Milner
  • Computer Science
    Lecture Notes in Computer Science
  • 1980
A case study in synchronization and proof techniques, and some proofs about data structures in value-communication as a model of CCS 2.0.
Towards a Lambda-Calculus for Concurrent and Communicating Systems
  • G. Boudol
  • Computer Science, Mathematics
    TAPSOFT, Vol.1
  • 1989
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.