procesalgebra

Procesalgebra, or process algebra in English, is a family of formal languages and semantic frameworks used to model and reason about concurrent systems. It treats processes as abstract entities that perform actions and interact through communication, providing a precise means to specify, compose, refine, and verify system behavior.

Core ideas are expressed through a small set of operators, such as action prefixing, alternative or choice, sequential and parallel composition, and operators for communication, restriction (hiding actions), and renaming. Recursion enables the representation of infinite or looping behavior. Equational laws and axioms define how complex processes can be simplified or transformed.

Semantics are typically given operationally by labeled transition systems or denotationally by mathematical structures. Behavioral equivalences such as strong and weak bisimulation, trace equivalence, and congruence under composition are used to determine when two processes are observationally the same in all contexts.

Prominent calculi include the Calculus of Communicating Systems (CCS) by Robin Milner, Communicating Sequential Processes (CSP) by Tony Hoare, the Algebra of Communicating Processes (ACP) by Bergstra and Klop, and the pi-calculus by Milner et al., which models mobility of communication links.

Process algebra has applications in formal verification, model checking, protocol design, and the analysis of distributed algorithms. It provides a foundation for reasoning about concurrency in programming languages and distributed systems, and it continues to influence related formalisms in concurrency theory.