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Probabilistic Simulations for Probabilistic Processes
, 1994
"... Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version o ..."
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Cited by 270 (18 self)
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Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.
Reactive, Generative and Stratified Models of Probabilistic Processes
 Information and Computation
, 1990
"... ion Let E; E 0 be PCCS expressions. The intermodel abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ..."
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Cited by 155 (7 self)
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ion Let E; E 0 be PCCS expressions. The intermodel abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ones, thereby abstracting away from the relative probabilities between different actions. We can now define 'GR ('G (P )) as the reactive transition system that can be inferred from P 's generative transition system via IMARGR . By the same procedure as described at the end of Section 3.1, 'GR can be extended to a mapping 'GR : j GG ! j GR . Write P GR ¸ Q if P; Q 2 Pr are reactive bisimulation equivalent with respect to the transitions derivable from G+IMARGR , i.e. the theory obtained by adding IMARGR to the rules of Figure 7. The equivalence GR ¸ is defined just like R ¸ but using the cPDF ¯GR instead of ¯R . ¯GR is defined by ¯GR (P; ff; S) = X i2I R (=I G ) fj p i j G+ I...
Bisimulation for Labelled Markov Processes
 Information and Computation
, 1997
"... In this paper we introduce a new class of labelled transition systems  Labelled Markov Processes  and define bisimulation for them. ..."
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Cited by 139 (23 self)
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In this paper we introduce a new class of labelled transition systems  Labelled Markov Processes  and define bisimulation for them.
Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
, 1998
"... . The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a ..."
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Cited by 75 (15 self)
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. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation. Keywords. Bisimulation, probabilistic transition system, coalgebra, ultrametric space, Borel measure, final coalgebra. 1 Introduction For discrete probabilistic transition systems the notion of probabilistic bisimilarity of Larsen and Skou [LS91] is regarded as the basic process equivalence. The definition was given for reactive systems. However, Van Glabbeek, Smolka and Steffen s...
Compositionality for probabilistic automata
 In Proc. 14th International Conference on Concurrency Theory (CONCUR 2003), volume 2761 of LNCS
, 2003
"... x ..."
A Logical Characterization of Bisimulation for Labeled Markov Processes
, 1998
"... This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [BDEP97]. The thrust of that work was an extension of the notion of bisimulation to systems with continuous state spaces; for example for systems where the state space is the real numbers. In ..."
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Cited by 34 (11 self)
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This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [BDEP97]. The thrust of that work was an extension of the notion of bisimulation to systems with continuous state spaces; for example for systems where the state space is the real numbers. In the present paper we study the logical characterization of probabilistic bisimulation for such general systems. This study revealed some unexpected results even for discrete probabilistic systems. ffl Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be characterized by several inequivalent logics; we report five in this paper. ffl We do not need any finite branching assumption yet there is no need of infinitary conjunction. ffl The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts abou...
Computing Minimum and Maximum Reachability Times in Probabilistic Systems
, 1999
"... A Markov decision process is a generalization of a Markov chain in which both probabilistic and nondeterministic choice coexist. Given a Markov decision process with costs associated with the transitions and a set of target states, the stochastic shortest path problem consists in computing the minim ..."
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Cited by 32 (2 self)
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A Markov decision process is a generalization of a Markov chain in which both probabilistic and nondeterministic choice coexist. Given a Markov decision process with costs associated with the transitions and a set of target states, the stochastic shortest path problem consists in computing the minimum expected cost of a control strategy that guarantees to reach the target. In this paper, we consider the classes of stochastic shortest path problems in which the costs are all nonnegative, or all nonpositive. Previously, these two classes of problems could be solved only under the assumption that the policies that minimize or maximize the expected cost also lead to the target with probability 1. This assumption does not necessarily hold for Markov decision processes that arise as model for distributed probabilistic systems. We present efficient methods for solving these two classes of problems without relying on additional assumptions. The methods are based on algorithms to transform th...
Comparative branchingtime semantics for Markov chains
 Information and Computation
, 2003
"... This paper presents various semantics in the branchingtime spectrum of discretetime and continuoustime Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilisti ..."
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Cited by 32 (12 self)
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This paper presents various semantics in the branchingtime spectrum of discretetime and continuoustime Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilistic Computation Tree Logic) and CSL (Continuous Stochastic Logic). Apart from presenting various existing branchingtime relations in a uniform manner, this paper presents the following new results: (i) strong simulation for CTMCs, (ii) weak simulation for CTMCs and DTMCs, (iii) logical characterizations thereof (including weak bisimulation for DTMCs), (iv) a relation between weak bisimulation and weak simulation equivalence, and (v) various connections between equivalences and preorders in the continuous and discretetime setting. The results are summarized in a branchingtime spectrum for DTMCs and CTMCs elucidating their semantics as well as their relationship. Key Words: comparative semantics, Markov chain, (weak) simulation, (weak) bisimulation, temporal logic
Probabilistic Automata: System Types, Parallel Composition and Comparison
 In Validation of Stochastic Systems: A Guide to Current Research
, 2004
"... We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other ha ..."
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Cited by 27 (5 self)
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We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other hand, it explains the relationship between these models.