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. 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 generated by the Kleene star).
The use of channels for communication is one of the features distinguishing the process calculi from other models of concurrency, such as Petri nets 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.
Read more about this topic: Process Calculus
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