nLab concurrency theory

Idea

In the theory of computation, concurrency (or maybe rather parallelism, cf. Harper 2011) refers to the situation of several (maybe interacting) processes proceeding simultaneously. Here the word “simultaneously” indicates that the evolution of the participating processes is indexed along an irreversible directed object.

Calculi

π-Calculus

With π-calculus, the processes can either be the nil process $0$, parallel execution $P \mid Q$, sending on channel $c$ and then continuing $\overline{c}\langle x \rangle.P$, receiving on channel $c$ and then continuing $c(x).P$, replicating a process $!P$ or introduction of a new name $(\nu x)P$.

$\rho$-Calculus

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Related entries

• parallel computing

• models for concurrency

• Directed Algebraic Topology and Concurrency

• Some geometric perspectives in concurrency theory

• in a wider sense also articles related to directed homotopy theory, cf.

  • Directed Algebraic Topology

  • directed homotopy type theory

References

• Wikipedia: Process calculus

• Wikipedia: Concurrency (computer science)

• Bob Harper: Parallelism is not concurrency (2011)

• Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen: Directed Algebraic Topology and Concurrency

• The Pi calculus: toward global computing Rchain (2019) [blog]

• Zoran Skoda: distributed consensus

category: computer science