 The axioms presented below comprise the full axiomatic system for ACPformula_3 (ACP with abstraction).Using the alternative and sequential composition operators, ACP defines a "basic process algebra" which satisfies the axioms

Beyond the basic algebra, two additional axioms define the relationships between the alternative and sequencing operators, and the "deadlock" action, formula_2

The axioms associated with the merge, left-merge, and communication operators are

When the communications operator is applied to actions alone, rather than processes, it is interpreted as a binary function from actions to actions, formula_42.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, formula_2, while permitted interaction pairs are mapped to corresponding single actions representing the occurrence of an interaction.