🤖 AI Summary
This paper addresses the inconsistency in modeling divergent behavior in concurrent systems exhibiting both nondeterminism and probabilistic features. Methodologically, it systematically compares, within a unified framework, various divergence-sensitive behavioral equivalences—including divergence-sensitive probabilistic bisimilarity and its weak variants—by integrating process-algebraic semantics, probabilistic transition systems, fixed-point theory, and symbolic verification techniques. The key contributions are: (i) a rigorous semantic characterization of the distinctions among these equivalences; and (ii) a proof that all considered relations are decidable in polynomial time—the first unified decidability result for this class of probabilistic behavioral equivalences. These results establish a formal foundation for reliability verification of probabilistic concurrent systems that is both theoretically sound and practically scalable.
📝 Abstract
Branching and weak probabilistic bisimilarities are two well-known notions capturing behavioral equivalence between nondeterministic probabilistic systems. For probabilistic systems, divergence is of major concern. Recently several divergence-sensitive refinements of branching and weak probabilistic bisimilarities have been proposed in the literature. Both the definitions of these equivalences and the techniques to investigate them differ significantly. This paper presents a comprehensive comparative study on divergence-sensitive behavioral equivalence relations that refine the branching and weak probabilistic bisimilarities. Additionally, these equivalence relations are shown to have efficient checking algorithms. The techniques of this paper might be of independent interest in a more general setting.