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16. 17. Computer Science, CWI Monograph 1, North-Holland, Amsterdam, 89138. A. W. KLOP (1986). Process algebra: specification and verification in bisimulation semantics. M. K. T. ). Mathematics and Computer Science II, CWI Monograph 4, North-Holland, Amsterdam, 61-94. A. W. K L O P (1986) Verification of an Alternating Bit Protocol by means of process algebra. W. P. ). Math. Methods of Spec, and Synthesis of Software Systems '85, Math. Research 31, Akademie-Verlag Berlin, 9-23. A. W. -R. OLDEROG (1987).

G/** is a model of all axioms in Tables 17 and 18. Remarkably, this graph model does not satisfy the unrestricted Approximation Induction Principle. A counterexample is given (in a self-explaining notation) by the two graphs g—^ n^\an and h =2n^\an +au; while g and h have the same finite projections tnn(g)= w/l(/r)= a+a2+a3 + • •Jra • n, they are not bisimilar due to the presence of the infinite trace of a-steps in h. It might be thought that it would be helpful to restrict the domain of process graphs to finitely branching graphs, in order to obtain a model which satisfies AIP, but there are two reasons why this is not the case: (1) the finitely branching graph domain would not be closed under the operations, in particular the communication merge (|); (2) a similar counterexample can be obtained by considering the finitely branching graphs g' = T{t}(g") where g" is the graph defined by n {X X \ l } andh'=g' + a°.

FIGURE PEn 1. Executing machine Here, every PEt is an autonomous process and each GMj one of the global variables. This machine is not only convenient for making calculations, it also exists in practice and is known as a common-bus system. 3. THE BASIC METHOD The method of proving the properties ME, LC and Li with process algebra is founded in a simple set of descriptions that restate the definitions of these properties in terms of process algebra. In the descriptions 9//CP), with H the set of sends and receives used to control the global variables and P the merge of all processes and global variables, denotes any legal state of the system, while 9#0P/) stands for the system obtained by removing process pt from P.

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