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52
A testing scenario for probabilistic processes
, 2006
"... We introduce a notion of finite testing, based on statistical hypothesis tests, via a variant of the wellknown trace machine. Under this scenario, two processes are deemed observationally equivalent if they cannot be distinguished by any finite test. We consider processes modeled as image finite pr ..."
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We introduce a notion of finite testing, based on statistical hypothesis tests, via a variant of the wellknown trace machine. Under this scenario, two processes are deemed observationally equivalent if they cannot be distinguished by any finite test. We consider processes modeled as image finite probabilistic automata and prove that our notion of observational equivalence coincides with the trace distribution equivalence proposed by Segala. Along the way, we give an explicit characterization of the set of probabilistic generalize the Approximation Induction Principle by defining an also prove limit and convex closure properties of trace distributions in an appropriate metric space. Categories and Subject Descriptors: F.1.1 [Computation by abstract devices]: Models of Computation—Automata; F.1.2 [Computation by abstract devices]: Modes of Computation—Probabilistic Computation; F.4.3 [Mathematical logic and formal languages]: Formal
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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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).
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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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
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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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
A Uniform Framework for Modeling Nondeterministic, Probabilistic, Stochastic, or Mixed Processes and their Behavioral Equivalences
, 2013
"... Labeled transition systems are typically used as behavioral models of concurrent processes. Their labeled transitions define a onestep statetostate reachability relation. This model can be generalized by modifying the transition relation to associate a state reachability distribution with any pai ..."
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Cited by 8 (4 self)
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Labeled transition systems are typically used as behavioral models of concurrent processes. Their labeled transitions define a onestep statetostate reachability relation. This model can be generalized by modifying the transition relation to associate a state reachability distribution with any pair consisting of a source state and a transition label. The state reachability distribution is a function mapping each possible target state to a value that expresses the degree of onestep reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture wellknown models of fully nondeterministic processes (LTS), fully probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. They can be defined on ULTraS by relying on appropriate measure functions that express the degree of reachability of a set of states when performing multistep computations. It is shown that the specializations of bisimulation, trace, and testing equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models except when nondeterminism and probability/stochasticity coexist; then new equivalences pop up.
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
Revisiting trace and testing equivalences for nondeterministic and probabilistic processes
 In Proc. of the 15th Int. Conf. on Foundations of Software Science and Computation Structures (FOSSACS 2012), volume 7213 of LNCS
, 2012
"... Abstract. Two of the most studied extensions of trace and testing equivalences to nondeterministic and probabilistic processes induce distinctions that have been questioned and lack properties that are desirable. Probabilistic tracedistribution equivalence differentiates systems that can perform ..."
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Abstract. Two of the most studied extensions of trace and testing equivalences to nondeterministic and probabilistic processes induce distinctions that have been questioned and lack properties that are desirable. Probabilistic tracedistribution equivalence differentiates systems that can perform the same set of traces with the same probabilities, and is not a congruence for parallel composition. Probabilistic testing equivalence, which relies only on extremal success probabilities, is backward compatible with testing equivalences for restricted classes of processes, such as fully nondeterministic processes or generative/reactive probabilistic processes, only if specific sets of tests are admitted. In this paper, new versions of probabilistic trace and testing equivalences are presented for the general class of nondeterministic and probabilistic processes. The new trace equivalence is coarser because it compares execution probabilities of single traces instead of entire trace distributions, and turns out to be compositional. The new testing equivalence requires matching all resolutions of nondeterminism on the basis of their success probabilities, rather than comparing only extremal success probabilities, and considers success probabilities in a tracebytrace fashion, rather than cumulatively on entire resolutions. It is fully backward compatible with testing equivalences for restricted classes of processes; as a consequence, the tracebytrace approach uniformly captures the standard probabilistic testing equivalences for generative and reactive probabilistic processes. The paper discusses in full details the new equivalences and provides a simple spectrum that relates them with existing ones in the setting of nondeterministic and probabilistic processes. 1.
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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Cited by 5 (2 self)
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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
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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Cited by 3 (1 self)
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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.
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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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...