Bounded nondeterminism and the approximation induction principle in process algebra
This paper presents a new semantics of ACPτ, the Algebra of Communicating Processes with abstraction. This leads to a term model of ACPτ which is isomorphic to the model of process graphs modulo rooted τδ-bisimulation of Baeten, Bergstra & Klop
In this model, the Recursive Definition Principle (RDP), the Commutativity of Abstraction (CA) and Koomen's Fair Abstraction Rule (KFAR) are satisfied, but the Approximation Induction Principle (AIP) is not. The combination of these four principles is proven to be inconsistent, while any combination of three of them is not.
In  a restricted version of AIP is proved valid in the graph model. This paper proposes a simpler and less restrictive version of AIP, not containing guarded recursive specifications as a parameter, which is still valid. This infinitary rule is formulated with the help of a family Bn of unary predicates, expressing bounded nondeterminism.
1980 Mathematics Subject Classification (version 1985)68Q10 68Q45 68Q55 68N15
1982 CR CategoriesF.1.2 F.3.2 F.4.3 D.3.1
Key Words & PhrasesConcurrency Process algebra ACP Approximation Induction Principle Recursion Abstraction Fairness Liveness Consistency Bisimulation Bounded Nondeterminism
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