the celebrated results are that the synchronous π-calculus is more expressive than its asynchronous variant, has the same expressive power as the higher-order π-calculus, but is less than the ambient calculus. Using process calculus to model biological systems (stochastic π-calculus, BioAmbients, Beta Binders, BioPEPA, Brane calculus). It is thought by some that the compositionality offered by process-theoretic tools can help biologists to organise their knowledge more formally. Software implementations The ideas behind process algebra have given rise to several tools including: CADP Concurrency Workbench mCRL2 toolset 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. See also Communicating sequential processes ProVerif Stochastic probe Tamarin Prover Temporal Process Language π-calculus References Further reading Matthew Hennessy: Algebraic Theory of Processes, The MIT Press, . C. A. R. Hoare: Communicating Sequential Processes, Prentice Hall, . This book has been updated by Jim Davies at the Oxford University Computing Laboratory and the new edition is available for download as a PDF file at the Using CSP website. Robin Milner: A Calculus of Communicating Systems, Springer Verlag, . Robin Milner: Communicating and Mobile Systems: the Pi-Calculus, Springer Verlag, .