Editing Process calculus (section)

== History ==

In the first half of the 20th century, various formalisms were proposed to capture the informal concept of a ''computable function'', with [[Μ-recursive function|&mu;-recursive functions]], [[Turing machine]]s  and the [[lambda calculus]] possibly being the best-known  examples today.  The surprising fact that they are essentially equivalent, in the sense that they are all encodable into each other, supports the [[Church-Turing thesis]].  Another shared feature is more rarely commented on: they all are most readily understood as models of ''sequential'' computation. The subsequent consolidation of computer science required a more subtle formulation of the notion of computation, in particular explicit representations of concurrency and communication. Models of concurrency such as the process calculi, [[Petri net]]s in 1962, and the [[actor model]] in 1973 emerged from this line of inquiry.

Research on process calculi began in earnest with [[Robin Milner]]'s seminal work on the [[Calculus of Communicating Systems]] (CCS) during the period from 1973 to 1980. [[C.A.R. Hoare]]'s [[Communicating Sequential Processes]] (CSP) first appeared in 1978, and was subsequently developed into a full-fledged process calculus during the early 1980s. There was much cross-fertilization of ideas between CCS and CSP as they developed. In 1982 [[Jan Bergstra]] and [[Jan Willem Klop]] began work on what came to be known as the [[Algebra of Communicating Processes]] (ACP), and introduced the term ''process algebra'' to describe their work.<ref name="baeten2004"/> CCS, CSP, and ACP constitute the three major branches of the process calculi family: the majority of the other process calculi can trace their roots to one of these three calculi.