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Testing finitary probabilistic processes. Full version of this extended abstract. Available at http://www.cse.unsw.edu.au/∼rvg/pub/finitary.pdf
, 2009
"... Abstract. We provide both modaland relational characterisations of mayand musttesting preorders for recursive CSP processes with divergence, featuring probabilistic as well as nondeterministic choice. May testing is characterised in terms of simulation, and must testing in terms of failure simul ..."
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Abstract. We provide both modaland relational characterisations of mayand musttesting preorders for recursive CSP processes with divergence, featuring probabilistic as well as nondeterministic choice. May testing is characterised in terms of simulation, and must testing in terms of failure simulation. To this end we develop weak transitions between probabilistic processes, elaborate their topological properties, and express divergence in terms of partial distributions.
A testing scenario for probabilistic processes
, 2007
"... 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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Cited by 14 (1 self)
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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.
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 11 (5 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
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 9 (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.
Kantorovich Metric in Computer Science: A Brief Survey
"... In contrast to its wealth of applications in mathematics, the Kantorovich metric started to be noticed in computer science only in recent years. We give a brief survey of its applications in probabilistic concurrency, image retrieval, data mining, and bioinformatics. This paper highlights the useful ..."
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Cited by 8 (1 self)
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In contrast to its wealth of applications in mathematics, the Kantorovich metric started to be noticed in computer science only in recent years. We give a brief survey of its applications in probabilistic concurrency, image retrieval, data mining, and bioinformatics. This paper highlights the usefulness of the Kantorovich metric as a general mathematical tool for solving various kinds of problems in rather unrelated domains.
Weighted bisimulations in linear algebraic form
, 2009
"... We study bisimulation and minimization for weighted automata, relying on a geometrical representation of the model, linear weighted automata (lwa). In a lwa, the statespace of the automaton is represented by a vector space, and the transitions and weighting maps by linear morphisms over this vect ..."
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Cited by 5 (1 self)
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We study bisimulation and minimization for weighted automata, relying on a geometrical representation of the model, linear weighted automata (lwa). In a lwa, the statespace of the automaton is represented by a vector space, and the transitions and weighting maps by linear morphisms over this vector space. Weighted bisimulations are represented by subspaces that are invariant under the transition morphisms. We show that the largest bisimulation coincides with weighted language equivalence, can be computed by a geometrical version of partition refinement and that the corresponding quotient gives rise to the minimal weightedlanguage equivalence automaton. Relations to Larsen and Skou’s probabilistic bisimulation and to classical results in Automata Theory are also discussed.
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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Cited by 5 (1 self)
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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
Marcaspis: a markovian extension of a calculus for services.
, 2008
"... Abstract Service Oriented Computing (SOC) is a design paradigm that has evolved from earlier paradigms including objectorientation and componentbased software engineering. Important features of services are compositionality, contextindependence, encapsulation and reusability. To support the for ..."
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Cited by 5 (4 self)
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Abstract Service Oriented Computing (SOC) is a design paradigm that has evolved from earlier paradigms including objectorientation and componentbased software engineering. Important features of services are compositionality, contextindependence, encapsulation and reusability. To support the formal design and analysis of SOC applications recently a number of Service Oriented Calculi have been proposed. Most of them are based on process algebras enriched with primitives specific of service orientation such as operators for manipulating semistructured data, mechanisms for describing safe clientservice interactions, constructors for composing possibly unreliable services and techniques for services query and discovery. In this paper we show a versatile technique for the definition of Structural Operational Semantics of MarCaSPiS, a Markovian extension of one of such calculi, namely the Calculus of Sessions and Pipelines, CaSPiS. The semantics deals in an elegant way with a stochastic version of twoparty synchronisation, typical of a serviceoriented approach, and with the problem of transition multiplicity while preserving highly desirable mathematical properties such as associativity and commutativity of parallel composition. We also show how the proposed semantics can be naturally used for defining a bisimulationbased behavioural equivalence for MarCaSPiS terms that induces the same equalities as those obtained via Strong Markovian Equivalence.
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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Cited by 5 (3 self)
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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.
Semantic Analysis of Gossip Protocols for Wireless Sensor Networks
"... Abstract. Gossip protocols have been proposed as a robust and efficient method for disseminating information throughout largescale networks. In this paper, we propose a compositional analysis technique to study formal probabilistic models of gossip protocols in the context of wireless sensor networ ..."
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Cited by 4 (0 self)
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Abstract. Gossip protocols have been proposed as a robust and efficient method for disseminating information throughout largescale networks. In this paper, we propose a compositional analysis technique to study formal probabilistic models of gossip protocols in the context of wireless sensor networks. We introduce a simple probabilistic timed process calculus for modelling wireless sensor networks. A simulation theory is developed to compare probabilistic protocols that have similar behaviour up to a certain probability. This theory is used to prove a number of algebraic laws which revealed to be very effective to evaluate the performances of gossip networks with and without communication collisions. 1