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Title:
BISIMULATIONS MEET PCTL EQUIVALENCES FOR PROBABILISTIC AUTOMATA
Author: Song, Lei ; Zhang, Lijun ; Godskesen, Jens Chr. ; Nielson, Flemming
Keyword: PCTL ; Probabilistic automata ; Characterization ; Bisimulation
Source: LOGICAL METHODS IN COMPUTER SCIENCE
Issued Date: 2013
Volume: 9, Issue:2
Indexed Type: SCI
Department: [Song, Lei; Zhang, Lijun] Saarland Univ Comp Sci, Saarbrucken, Germany. [Zhang, Lijun] Tech Univ Denmark, DTU Informat, Chinese Acad Sci, State Key Lab Comp Sci,Inst Software, Lyngby, Denmark. [Godskesen, Jens Chr.] IT Univ Copenhagen, Copenhagen, Denmark. [Nielson, Flemming] Tech Univ Denmark, DTU Compute, Lyngby, Denmark.
Abstract: Probabilistic automata (PAs) have been successfully applied in formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are based on probabilistic computation tree logic (PCTL) and its extension PCTL*. Various behavioral equivalences are proposed, as a powerful tool for abstraction and compositional minimization for PAs. Unfortunately, the equivalences are well-known to be sound, but not complete with respect to the logical equivalences induced by PCTL or PCTL*. The desire of a both sound and complete behavioral equivalence has been pointed out by Segala in [34], but remains open throughout the years. In this paper we introduce novel notions of strong bisimulation relations, which characterize PCTL and PCTL* exactly. We extend weak bisimulations that characterize PCTL and PCTL* without next operator, respectively. Further, we also extend the framework to simulation preorders. Thus, our paper bridges the gap between logical and behavioral equivalences and preorders in this setting.
English Abstract: Probabilistic automata (PAs) have been successfully applied in formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are based on probabilistic computation tree logic (PCTL) and its extension PCTL*. Various behavioral equivalences are proposed, as a powerful tool for abstraction and compositional minimization for PAs. Unfortunately, the equivalences are well-known to be sound, but not complete with respect to the logical equivalences induced by PCTL or PCTL*. The desire of a both sound and complete behavioral equivalence has been pointed out by Segala in [34], but remains open throughout the years. In this paper we introduce novel notions of strong bisimulation relations, which characterize PCTL and PCTL* exactly. We extend weak bisimulations that characterize PCTL and PCTL* without next operator, respectively. Further, we also extend the framework to simulation preorders. Thus, our paper bridges the gap between logical and behavioral equivalences and preorders in this setting.
Language: 英语
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16699
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Song, Lei,Zhang, Lijun,Godskesen, Jens Chr.,et al. BISIMULATIONS MEET PCTL EQUIVALENCES FOR PROBABILISTIC AUTOMATA[J]. LOGICAL METHODS IN COMPUTER SCIENCE,2013-01-01,9(2).
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