A complete equational axiomatization for prefix iteration
Information Processing Letters
Axiomatizing prefix iteration with silent steps
Information and Computation
Branching time and abstraction in bisimulation semantics
Journal of the ACM (JACM)
Communication and Concurrency
On the Completeness of the Euations for the Kleene Star in Bisimulation
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
The Linear Time - Branching Time Spectrum II
CONCUR '93 Proceedings of the 4th International Conference on Concurrency Theory
Information and Computation
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We study the divergent-sensitive spectrum of weak bisimulation equivalences in the setting of process algebra. To represent the infinite behavior, we consider the prefix iteration extension of a fragment of Milner's CCS. The prefix iteration operator is a variant on the binary version of the Kleene star operator obtained by restricting the first argument to be an atomic action and allows us to capture the notion of recursion in a pure algebraic way. We investigate four typical divergent-sensitive weak bisimulation equivalences, namely divergent, stable, completed and divergent stable weak bisimulation equivalences from an axiomatic perspective. A lattice of distinguishing axioms is developed and thus pure equational axiomatizations for these congruences are obtained. A large part of the current paper is devoted to a considerable complicated proof for completeness. This work, to some extent, sheds light on distinct semantics of divergence.