ACP was initially developed by Jan Bergstra and Jan Willem Klop in 1982,[1] as part of an effort to investigate the solutions of unguarded recursive equations.
This algebra is a way to describe systems in terms of algebraic process expressions that define compositions of other processes, or of certain primitive elements.
Actions can be combined to form processes using a variety of operators.
These operators can be roughly categorized as providing a basic process algebra, concurrency, and communication.
ACP fundamentally adopts an axiomatic, algebraic approach to the formal definition of its various operators.
The axioms presented below comprise the full axiomatic system for ACP
Using the alternative and sequential composition operators, ACP defines a basic process algebra which satisfies the axioms[3] Beyond the basic algebra, two additional axioms define the relationships between the alternative and sequencing operators, and the deadlock action,
The definition of this function defines the possible interactions between processes — those pairs of actions that do not constitute interactions are mapped to the deadlock action,
, which is used to convert unsuccessful communication attempts (i.e. elements of
The axioms associated with the communications function and encapsulation operator are[3] The axioms associated with the abstraction operator are[3] Note that the action a in the above list may take the value δ (but of course, δ cannot belong to the abstraction set I).
ACP has served as the basis or inspiration for several other formalisms that can be used to describe and analyze concurrent systems, including: