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Testing Finitary Probabilistic Processes (Extended Abstract)
"... Abstract. This paper provides modal and 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 si ..."
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Abstract. This paper provides modal and 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 capture divergence in terms of partial distributions. 1
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
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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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 2 (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.
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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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
A Local Algorithm for Checking Probabilistic Bisimilarity
"... Abstract—Bisimilarity is one of the most important relations for comparing the behaviour of formal systems in concurrency theory. Decision algorithms for bisimilarity in finite state systems are usually classified into two kinds: global algorithms are generally efficient but require to generate the ..."
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Abstract—Bisimilarity is one of the most important relations for comparing the behaviour of formal systems in concurrency theory. Decision algorithms for bisimilarity in finite state systems are usually classified into two kinds: global algorithms are generally efficient but require to generate the whole state spaces in advance, and local algorithms combine the verification of a system’s behaviour with the generation of the system’s state space, which is often more effective to determine that one system fails to be related to another. Although local algorithms are well established in the classical concurrency theory, the study of local algorithms in probabilistic concurrency theory is not mature. In this paper we propose a polynomial time local algorithm for checking probabilistic bisimilarity. With mild modification, the algorithm can be easily adapted to decide probabilistic similarity with the same time complexity. Keywordsconcurrency; probabilistic bisimilarity; local algorithm; probabilistic labelled transition systems; I.
Relating Reasoning Methodologies in Linear Logic and Process Algebra
, 2011
"... We show that the prooftheoretic notion of logical preorder coincides with the processtheoretic notion of contextual preorder for a CCSlike process calculus obtained from the formulaasprocess interpretation of a fragment of linear logic. The argument makes use of other standard notions in proces ..."
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We show that the prooftheoretic notion of logical preorder coincides with the processtheoretic notion of contextual preorder for a CCSlike process calculus obtained from the formulaasprocess interpretation of a fragment of linear logic. The argument makes use of other standard notions in process algebra, namely simulation and labeled transition systems. This result establishes a connection between an approach to reason about process specifications, the contextual preorder, and a method to reason about logic specifications, the logical preorder.
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
Under consideration for publication in Formal Aspects of Computing Characterisations of Testing Preorders for a Finite Probabilistic πCalculus
"... Abstract. We consider two characterisations of the may and must testing preorders for a probabilistic extension of the finite πcalculus: one based on notions of probabilistic weak simulations, and the other on a probabilistic extension of a fragment of MilnerParrowWalker modal logic for the πcal ..."
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Abstract. We consider two characterisations of the may and must testing preorders for a probabilistic extension of the finite πcalculus: one based on notions of probabilistic weak simulations, and the other on a probabilistic extension of a fragment of MilnerParrowWalker modal logic for the πcalculus. We base our notions of simulations on similar concepts used in previous work for probabilistic CSP. However, unlike the case with CSP (or other nonvaluepassing calculi), there are several possible definitions of simulation for the probabilistic πcalculus, which arise from different ways of scoping the name quantification. We show that in order to capture the testing preorders, one needs to use the “earliest ” simulation relation (in analogy to the notion of early (bi)simulation in the nonprobabilistic case). The key ideas in both characterisations are the notion of a “characteristic formula ” of a probabilistic process, and the notion of a “characteristic test ” for a formula. As in an earlier work on testing equivalence for the πcalculus by Boreale and De Nicola, we extend the language of the πcalculus with a mismatch operator, without which the formulation of a characteristic test will not be possible.
Testing Probabilistic Processes: Can Random Choices Be Unobservable?
, 907
"... Abstract. A central paradigm behind process semantics based on observability and testing is that the exact moment of occurring of an internal nondeterministic choice is unobservable. It is natural, therefore, for this property to hold when the internal choice is quantified with probabilities. Howeve ..."
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Abstract. A central paradigm behind process semantics based on observability and testing is that the exact moment of occurring of an internal nondeterministic choice is unobservable. It is natural, therefore, for this property to hold when the internal choice is quantified with probabilities. However, ever since probabilities have been introduced in process semantics, it has been a challenge to preserve the unobservability of the random choice, while not violating the other laws of process theory and probability theory. This paper addresses this problem. It proposes two semantics for processes where the internal nondeterminism has been quantified with probabilities. The first one is based on the notion of testing, i.e. interaction between the process and its environment. The second one, the probabilistic ready trace semantics, is based on the notion of observability. Both are shown to coincide. They are also preserved under the standard operators. 1