Algebra of communicating processes with abstraction

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Jan A. Bergstra, Jan Willem Klop
Theoretical Computer Science 37, pages 77121

<div>We present an axiom system ACP, for communicating processes with silent actions (‘&tau;-steps’). The system is an extension of ACP, Algebra of Communicating Processes, with Milner's &tau;-laws and an explicit abstraction operator. By means of a model of finite acyclic process graphs for ACP<sub>&tau;</sub>, syntactic properties such as consistency and conservativity over ACP are proved. Furthermore, the Expansion Theorem for ACP is shown to carry over to ACP<sub>&tau;</sub>. Finally, termination of rewriting terms according to the ACP<sub>&tau;</sub>, axioms is probed using the method of recursive path orderings.</div>