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A menagerie of nonfinitely based process semantics over BPA*—from ready simulation to completed traces
 Mathematical Structures in Computer Science
, 1998
"... Fokkink and Zantema ((1994) Computer Journal 37:259–267) have shown that bisimulation equivalence has a finite equational axiomatization over the language of Basic Process Algebra with the binary Kleene star operation (BPA ∗). In the light of this positive result on the mathematical tractability of ..."
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Cited by 24 (19 self)
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Fokkink and Zantema ((1994) Computer Journal 37:259–267) have shown that bisimulation equivalence has a finite equational axiomatization over the language of Basic Process Algebra with the binary Kleene star operation (BPA ∗). In the light of this positive result on the mathematical tractability of bisimulation equivalence over BPA ∗ , a natural question to ask is whether any other (pre)congruence relation in van Glabbeek’s linear time/branching time spectrum is finitely (in)equationally axiomatizable over it. In this paper, we prove that, unlike bisimulation equivalence, none of the preorders and equivalences in van Glabbeek’s linear time/branching time spectrum, whose discriminating power lies in between that of ready simulation and that of completed traces, has a finite equational axiomatization. This we achieve by exhibiting a family of (in)equivalences that holds in ready simulation semantics, the finest semantics that we consider, whose instances cannot all be proven by means of any finite set of (in)equations
Equational axioms for probabilistic bisimilarity
 IN PROCEEDINGS OF 9TH AMAST, LECTURE NOTES IN COMPUTER SCIENCE
, 2002
"... This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finitestate agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571595). The axiomatization is obtained by extending ..."
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Cited by 17 (0 self)
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This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finitestate agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (#)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity.