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44
Logical, Metric, and Algorithmic Characterisations of Probabilistic Bisimulation
, 2011
"... Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states. We show that several existing proposals for lifting relations can be reconciled to be different presentations of essentially ..."
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Cited by 6 (2 self)
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Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states. We show that several existing proposals for lifting relations can be reconciled to be different presentations of essentially the same lifting operation. More interestingly, this lifting operation nicely corresponds to the Kantorovich metric, a fundamental concept used in mathematics to lift a metric on states to a metric on distributions of states, besides the fact the lifting operation is related to the maximum flow problem in optimisation theory. The lifting operation yields a neat notion of probabilistic bisimulation, for which we provide logical, metric, and algorithmic characterisations. Specifically, we extend the HennessyMilner logic and the modal mucalculus with a new modality, resulting in an adequate and an expressive logic for probabilistic bisimilarity, respectively. The correspondence of the lifting operation and the Kantorovich metric leads to a natural characterisation of bisimulations as pseudometrics which are postfixed points of a monotone function. We also present an “on the fly ” algorithm to check if two states in a finitary system are related by probabilistic bisimilarity, exploiting the close relationship
Metric semantics for reactive probabilistic processes
, 1997
"... In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these syst ..."
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In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these systems. Two processes are identified with respect to this equivalence if, for all experiments, the probabilities of the respective processes passing a given experiment are equal. We next consider a probabilistic process calculus including external choice, internal choice, actionguarded probabilistic choice, synchronous parallel and recursion. We give operational semantics for this calculus be means of our generalised labelled transition systems and show that our equivalence is a congruence for this language. Following the methodology introduced by de Bakker & Zucker, we then give denotational semantics to the calculus by means of a complete metric space of probabilistic processes. The derived metric, although not an ultrametric, satisfies the intuitive property that the distance between two processes tends to 0 if a measure of the dif
Trace Machines for Observing ContinuousTime Markov Chains
 in Proc. of the 3rd Int. Workshop on Quantitative Aspects of Programming Languages (QAPL 2005), ENTCS
, 2005
"... In this paper, we study several lineartime equivalences (Markovian trace equivalence, failure and ready trace equivalence) for continuoustime Markov chains that refer to the probabilities for timed execution paths. Our focus is on testing scenarios by means of pushbutton experiments with appropri ..."
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Cited by 6 (1 self)
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In this paper, we study several lineartime equivalences (Markovian trace equivalence, failure and ready trace equivalence) for continuoustime Markov chains that refer to the probabilities for timed execution paths. Our focus is on testing scenarios by means of pushbutton experiments with appropriate trace machines and a discussion of the connections between the equivalences. For Markovian trace equivalence, we provide alternative characterizations, including one that abstracts away from the time instances where actions are observed, but just reports on the average sojourn times in the states. This result is used for a reduction of the question whether two finitestate continuoustime Markov chains are Markovian trace equivalent to the probabilistic trace equivalence problem for discretetime Markov chains (and the latter is known to be solvable in polynomial time).
A Survey of Markovian Behavioral Equivalences
"... Abstract. Markovian behavioral equivalences are a means to relate and manipulate the formal descriptions of systems with an underlying CTMC semantics. There are three fundamental approaches to their definition: bisimilarity, testing, and trace. In this paper we survey the major results appeared in t ..."
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Cited by 5 (0 self)
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Abstract. Markovian behavioral equivalences are a means to relate and manipulate the formal descriptions of systems with an underlying CTMC semantics. There are three fundamental approaches to their definition: bisimilarity, testing, and trace. In this paper we survey the major results appeared in the literature about Markovian bisimilarity, Markovian testing equivalence, and Markovian trace equivalence. The objective is to compare these equivalences with respect to a number of criteria such as their discriminating power, the exactness of the CTMClevel aggregations they induce, the achievement of the congruence property, the existence of sound and complete axiomatizations, the existence of logical characterizations, and the existence of efficient verification algorithms. 1
Partial Order Models for Quantitative Extensions of LOTOS
, 1997
"... Event structures are a prominent model for noninterleaving concurrency. The use of event structures for providing a compositional noninterleaving semantics to LOTOS without data is studied. In particular, several quantitative extensions of event structures are proposed that incorporate notions lik ..."
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Cited by 3 (1 self)
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Event structures are a prominent model for noninterleaving concurrency. The use of event structures for providing a compositional noninterleaving semantics to LOTOS without data is studied. In particular, several quantitative extensions of event structures are proposed that incorporate notions like timeboth of deterministic and stochastic natureand probability. The suitability of these models for giving a noninterleaving semantics to a timed, stochastic and probabilistic extension of LOTOS is investigated. Consistency between the event structure semantics and an (eventbased) operational semantics is addressed for the different quantitative variants of LOTOS and is worked out for the timed case in more detail. These consistency results facilitate the coherent use of an interleaving and a noninterleaving semantic view in a single design trajectory and provide a justification for the event structure semantics. As a running example an infinite buffer is used in which gradually t...
Probabilistic Environments in the Quantitative Analysis of (NonProbabilistic) Behaviour Models
"... System specifications have long been expressed through automatabased languages, enabling verification techniques such as model checking. These verification techniques can assess whether a property holds or not, given a system specification. Quantitative model checking can provide additional informa ..."
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System specifications have long been expressed through automatabased languages, enabling verification techniques such as model checking. These verification techniques can assess whether a property holds or not, given a system specification. Quantitative model checking can provide additional information on the probability of these properties holding. We are interested in quantitatively analysing the probability of errors in nonprobabilistic system models by composing them with probabilistic models of the environment. Although many probabilistic automatabased formalisms and composition operators exist, these are not adequate for such a setting. In this work we present a formalism inspired on interface automata and a suitable composition operator for these automata that enables validation of environment models in isolation and sound analysis of its composition with the nonprobabilistic model of the systemunderanalysis.
An Axiomatization of Probabilistic Testing
, 1999
"... In this paper we present a sound and complete axiom system for a probabilistic process algebra with recursion. Soundness and completeness of the axiomatization is given with respect to the testing semantics defined in [19]. ..."
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Cited by 2 (1 self)
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In this paper we present a sound and complete axiom system for a probabilistic process algebra with recursion. Soundness and completeness of the axiomatization is given with respect to the testing semantics defined in [19].
Taking Chances on  and fail: Extending Strong and Probabilistic Bisimulation
, 1999
"... For a process language, featuring nondeterministic and probabilistic choice, a parallel operator and a failure construct, a notion of bisimulation is proposed. As one can interpret recovery from failure with respect to nondeterministic and probabilistic choice in various ways, a single transition sy ..."
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For a process language, featuring nondeterministic and probabilistic choice, a parallel operator and a failure construct, a notion of bisimulation is proposed. As one can interpret recovery from failure with respect to nondeterministic and probabilistic choice in various ways, a single transition system gives rise to several operational models. A uniform way to abstract the `first steps' underlies, for each of these models, the definition of the proposed bisimulation. This bisimulation specializes to ParkMilner bisimulation for the nonprobabilistic fragment of the language on the one hand, and to LarsenSkou bisimulation for the deterministic/probabilistic part of the language, on the other hand. Furthermore, a conditional congruence result is obtained. 1 Introduction Understanding the interplay of nondeterminacy and probability is a key issue in the development of formal techniques for specification and validation of probabilistic programs and protocols. In this paper we study a pr...
Characterising probabilistic processes logically
, 2009
"... Abstract. In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mucalculus and show how to derive characteristic formulae for various simulationlike preorders over finitestat ..."
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Abstract. In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mucalculus and show how to derive characteristic formulae for various simulationlike preorders over finitestate processes without divergence. In addition, we show that even without the fixpoint operators this probabilistic mucalculus can be used to characterise these behavioural relations in the sense that two states are equivalent if and only if they satisfy the same set of formulae. 1
Fair Testing Through Probabilistic Testing
, 1999
"... In this paper we define a probabilistic testing semantics which can be used to alternatively characterize fair testing. The key idea is to define a probabilistic semantics in such a way that two nonprobabilistic processes are fair equivalent iff any probabilistic version of both processes are equiv ..."
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In this paper we define a probabilistic testing semantics which can be used to alternatively characterize fair testing. The key idea is to define a probabilistic semantics in such a way that two nonprobabilistic processes are fair equivalent iff any probabilistic version of both processes are equivalent in our probabilistic testing semantics. In order to get this result we define a simple probabilistic must semantics by saying that a probabilistic process must pass a test iff the probability with which the process passes the test equals 1. Finally, we present an algorithm for deciding whether the probability with which a finitestate process passes a finitestate test equals 1. Alternatively, this algorithm can be used for computing whether a finitestate process fairly passes a finitestate test. Keywords: Testing semantics, fair testing, probabilistic processes. 1. INTRODUCTION Formal models of concurrency have been proved to be very useful to properly specify concurrent and distr...