Pure bigraphs : Structure and dynamics

J.A. BERGSTRA and J.W. KLOP Centre for Mathematics and Computer Science, P. O. Box 4079, 1009 AB Amsterdam, The Netherlands Communicated by E. Engeler Received February 1984 Revised October 1984 Abstract. We present an axiom system ACP, for communicating processes with silent actions ('z-steps'). The system is an extension o f ACP, Algebra of Communicating Processes, with Milner's z-laws and an explicit abstraction operator. By means of a model of finite acyclic process graphs for A C P , syntactic properties such as consistency and conservativity over ACP are proved. Furthermore, the Expansion Theorem for ACP is shown to carry over to ACP~. Finally, termination of rewriting terms according to the ACP~ axioms is proved using the method of recursive path orderings. We present an axiom system ACP, for communicating processes with silent actions ('z-steps'). The system is an extension o f ACP, Algebra of Communicating Processes, with Milner's z-laws and an explicit abstraction operator. By means of a model of finite acyclic process graphs for A C P , syntactic properties such as consistency and conservativity over ACP are proved. Furthermore, the Expansion Theorem for ACP is shown to carry over to ACP~. Finally, termination of rewriting terms according to the ACP~ axioms is proved using the method of recursive path orderings.