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12
Logical Characterizations of Bisimulations for Discrete Probabilistic Systems
, 2007
"... We give logical characterizations of bisimulation relations for the probabilistic automata of Segala in terms of three HennessyMilner style logics. The three logics characterize strong, strong probabilistic and weak probabilistic bisimulation, and differ only for the kind of diamond operator used. ..."
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We give logical characterizations of bisimulation relations for the probabilistic automata of Segala in terms of three HennessyMilner style logics. The three logics characterize strong, strong probabilistic and weak probabilistic bisimulation, and differ only for the kind of diamond operator used. Compared to the Larsen and Skou logic for reactive systems, these logics introduce a new operator that measures the probability of the set of states that satisfy a formula. Moreover, the satisfaction relation is defined on measures rather than single states. We rederive previous results of Desharnais et. al. by defining sublogics for Reactive and Alternating Models viewed as restrictions of probabilistic automata. Finally, we identify restrictions on probabilistic automata, weaker than those imposed by the Alternating Models, that preserve the logical characterization of Desharnais et. al. These restrictions require that each state either enables several ordinary transitions or enables a single probabilistic transition.
Partial Order Reduction For Probabilistic Branching Time
, 2005
"... In the past, partial order reduction has been used successfully to combat the state explosion problem in the context of model checking for nonprobabilistic systems. For both linear time and branching time specifications, methods have been developed to apply partial order reduction in the context of ..."
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Cited by 10 (3 self)
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In the past, partial order reduction has been used successfully to combat the state explosion problem in the context of model checking for nonprobabilistic systems. For both linear time and branching time specifications, methods have been developed to apply partial order reduction in the context of model checking. Only recently, results were published that give criteria on applying partial order reduction for verifying quantitative linear time properties for probabilistic systems. This paper presents partial order reduction criteria for Markov decision processes and branching time properties, such as formulas of probabilistic computation tree logic. Moreover, we provide a comparison of the results established so far about reduction conditions for Markov decision processes.
On the Semantics of Markov Automata
"... Abstract. Markov automata describe systems in terms of events which may be nondeterministic, may occur probabilistically, or may be subject to time delays. We define a novel notion of weak bisimulation for such systems and prove that this provides both a sound and complete proof methodology for a na ..."
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Cited by 6 (3 self)
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Abstract. Markov automata describe systems in terms of events which may be nondeterministic, may occur probabilistically, or may be subject to time delays. We define a novel notion of weak bisimulation for such systems and prove that this provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between such systems, a generalisation of reduction barbed congruence, the wellknown touchstone equivalence for a large variety of process description languages. 1
Concurrency and Composition in a Stochastic World
, 2012
"... Abstract. We discuss conceptional and foundational aspects of Markov automata [22]. We place this model in the context of continuous and discretetime Markov chains, probabilistic automata and interactive Markov chains, and provide insight into the parallel execution of such models. We further give ..."
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Cited by 3 (1 self)
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Abstract. We discuss conceptional and foundational aspects of Markov automata [22]. We place this model in the context of continuous and discretetime Markov chains, probabilistic automata and interactive Markov chains, and provide insight into the parallel execution of such models. We further give a detailled account of the concept of relations on distributions, and discuss how this can generalise known notions of weak simulation and bisimulation, such as to fuse sequences of internal transitions. 1
Weak Bisimulation for ActionType Coalgebras
"... A coalgebraic definition of weak bisimulation is proposed for a class of coalgebras obtained from bifunctors in Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The transformation consists of two steps: First, the behaviour on actions is expanded to beh ..."
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Cited by 2 (1 self)
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A coalgebraic definition of weak bisimulation is proposed for a class of coalgebras obtained from bifunctors in Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The transformation consists of two steps: First, the behaviour on actions is expanded to behaviour on finite words. Second, the behaviour on finite words is taken modulo the hiding of invisible actions, yielding behaviour on equivalence classes of words closed under silent steps. The coalgebraic definition is justified by two correspondence results, one for the classical notion of weak bisimulation of Milner and another for the notion of weak bisimulation for generative probabilistic transition systems as advocated by Baier and Hermanns.
A Companion to Coalgebraic Weak Bisimulation for ActionType Systems ∗
"... We propose a coalgebraic definition of weak bisimulation for classes of coalgebras obtained from bifunctors in the category Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The particular transformation consists of two steps: First, the behavior on acti ..."
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Cited by 1 (0 self)
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We propose a coalgebraic definition of weak bisimulation for classes of coalgebras obtained from bifunctors in the category Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The particular transformation consists of two steps: First, the behavior on actions is lifted to behavior on finite words. Second, the behavior on finite words is taken modulo the hiding of internal or invisible actions, yielding behavior on equivalence classes of words closed under silent steps. The coalgebraic definition is validated by two correspondence results: one for the classical notion of weak bisimulation of Milner, another for the notion of weak bisimulation for generative probabilistic transition systems as advocated by Baier and Hermanns. 1
A Spectrum of Behavioral Relations over LTSs on Probability Distributions
"... Abstract. Probabilistic nondeterministic processes are commonly modeled as probabilistic LTSs (PLTSs, a.k.a. probabilistic automata). A number of logical characterizations of the main behavioral relations on PLTSs have been studied. In particular, Parma and Segala [2007] define a probabilistic Henne ..."
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Abstract. Probabilistic nondeterministic processes are commonly modeled as probabilistic LTSs (PLTSs, a.k.a. probabilistic automata). A number of logical characterizations of the main behavioral relations on PLTSs have been studied. In particular, Parma and Segala [2007] define a probabilistic HennessyMilner logic interpreted over distributions, whose logical equivalence/preorder when restricted to Dirac distributions coincide with standard bisimulation/simulation between the states of a PLTS. This result is here extended by studying the full logical equivalence/preorder between distributions in terms of a notion of bisimulation/simulation defined on a LTS of probability distributions (DLTS). We show that the standard spectrum of behavioral relations on nonprobabilistic LTSs as well as its logical characterization in terms of HennessyMilner logic scales to the probabilistic setting when considering DLTSs. 1
On Compositionality, Efficiency, and Applicability of Abstraction in Probabilistic Systems
"... Abstract. A branching bisimulation for probabilistic systems that is preserved under parallel composition has been defined recently for the alternating model. We show that besides being compositional, it is decidable in polynomial time and it preserves the properties expressible in probabilistic Com ..."
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Abstract. A branching bisimulation for probabilistic systems that is preserved under parallel composition has been defined recently for the alternating model. We show that besides being compositional, it is decidable in polynomial time and it preserves the properties expressible in probabilistic Computation Tree Logic (pCTL). In the groundcomplete axiomatization, only a single axiom is added to the axioms for strong bisimulation. We show that the Concurrent Alternating Bit protocol can be verified using the process algebra and a set of recursive rules. 1
Model Checking for a Class of Performance Properties of Fluid Stochastic Models
"... Abstract. Recently, there is an explosive development of fluid approaches to computer and distributed systems. These approaches are inherently stochastic and generate continuous state space models. Usually, the performance measures for these systems are defined using probabilities of reaching certai ..."
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Abstract. Recently, there is an explosive development of fluid approaches to computer and distributed systems. These approaches are inherently stochastic and generate continuous state space models. Usually, the performance measures for these systems are defined using probabilities of reaching certain sets of the state space. These measures are well understood in the discrete context and many efficient model checking procedures have been developed for specifications involving them. The continuous case is far more complicated and new methods are necessary. In this paper we propose a general model checking strategy founded on advanced concepts and results of stochastic analysis. Due to the problem complexity, in this paper, we achieve the first necessary step of characterizing mathematically the problem. We construct upper bounds for the performance measures using Martin capacities. We introduce a concept of bisimulation that preserves the performance measures and a metric that characterizes the bisimulation.