Editing Process calculus (section)

== Relationship to other models of concurrency ==
The [[history monoid]] is the [[free object]] that is generically able to represent the histories of individual communicating processes. A process calculus is then a [[formal language]] imposed on a history monoid in a consistent fashion.<ref>{{cite book | first = Antoni | last = Mazurkiewicz | chapter-url = http://www.ipipan.waw.pl/~amaz/papers.htm/trbook.ps | chapter-format = PostScript | chapter = Introduction to Trace Theory | pages = 3–41 | title = The Book of Traces | editor1-first = V. | editor1-last = Diekert | editor2-first = G. | editor2-last = Rozenberg | year = 1995 | publisher = World Scientific | location = Singapore | isbn = 981-02-2058-8 | access-date = 2009-04-29 | archive-date = 2011-06-13 | archive-url = https://web.archive.org/web/20110613105701/http://www.ipipan.waw.pl/~amaz/papers.htm/trbook.ps | url-status = dead }}</ref> That is, a history monoid can only record a sequence of events, with synchronization, but does not specify the allowed state transitions. Thus, a process calculus is to a history monoid what a formal language is to a [[free monoid]] (a formal language is a subset of the set of all possible finite-length strings of an [[alphabet (computer science)|alphabet]] generated by the [[Kleene star]]).

The use of channels for communication is one of the features distinguishing the process calculi from other models of [[Concurrent computing|concurrency]], such as [[Petri net]]s and the [[actor model]] (see [[Actor model and process calculi]]). One of the fundamental motivations for including channels in the process calculi was to enable certain algebraic techniques, thereby making it easier to reason about processes algebraically.