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Nondeterministic labeled Markov processes: Bisimulations and logical characterizations
 In Proc. of the 6th Int. Conf. on the Quantitative Evaluation of Systems (QEST 2009
, 2009
"... We extend the theory of labeled Markov processes with internal nondeterminism, a fundamental concept for the further development of a process theory with abstraction on nondeterministic continuous probabilistic systems. We define nondeterministic labeled Markov processes (NLMP) and provide both a s ..."
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We extend the theory of labeled Markov processes with internal nondeterminism, a fundamental concept for the further development of a process theory with abstraction on nondeterministic continuous probabilistic systems. We define nondeterministic labeled Markov processes (NLMP) and provide both a state based bisimulation and an event based bisimulation. We show the relation between them, including that the largest state bisimulation is also an event bisimulation. We also introduce a variation of the HennessyMilner logic that characterizes event bisimulation and that is sound w.r.t. the state base bisimulation for arbitrary NLMP. This logic, however, is infinitary as it contains a denumerable ∨. We then introduce a finitary sublogic that characterize both state and event bisimulation for image finite NLMP whose underlying measure space is also analytic. Hence, in this setting, all notions of bisimulation we deal with turn out to be equal. 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
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
Simulation and Bisimulation for Probabilistic Timed Automata
"... Probabilistic timed automata are an extension of timed automata with discrete probability distributions. Simulation and bisimulation relations are widelystudied in the context of the analysis of system models, with applications in the stepwise development of systems and in model reduction. In this ..."
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Probabilistic timed automata are an extension of timed automata with discrete probability distributions. Simulation and bisimulation relations are widelystudied in the context of the analysis of system models, with applications in the stepwise development of systems and in model reduction. In this paper, we study probabilistic timed simulation and bisimulation relations for probabilistic timed automata. We present an EXPTIME algorithm for deciding whether two probabilistic timed automata are probabilistically timed similar or bisimilar. Furthermore, we consider a logical characterization of probabilistic timed bisimulation.
On probabilistic alternating simulations
, 2010
"... Abstract. This paper presents simulationbased relations for probabilistic game structures. The first relation is called probabilistic alternating simulation, and the second called probabilistic alternating forward simulation, following the naming convention of Segala and Lynch. We study these re ..."
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Abstract. This paper presents simulationbased relations for probabilistic game structures. The first relation is called probabilistic alternating simulation, and the second called probabilistic alternating forward simulation, following the naming convention of Segala and Lynch. We study these relations with respect to the preservation of properties specified in probabilistic alternatingtime temporal logic. 1
Probabilistic Bisimulation and Simulation Algorithms by Abstract Interpretation
"... Abstract. We show how bisimulation equivalence and simulation preorder on probabilistic LTSs (PLTSs), namely the main behavioural relations on probabilistic nondeterministic processes, can be characterized by abstract interpretation. Both bisimulation and simulation can be obtained as completions of ..."
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Abstract. We show how bisimulation equivalence and simulation preorder on probabilistic LTSs (PLTSs), namely the main behavioural relations on probabilistic nondeterministic processes, can be characterized by abstract interpretation. Both bisimulation and simulation can be obtained as completions of partitions and preorders, viewed as abstract domains, w.r.t. a pair of concrete functions that encode a PLTS. As a consequence, this approach provides a general framework for designing algorithms for computing bisimulation and simulation on PLTSs. Notably, (i) we show that the standard bisimulation algorithm by Baier et al. can be viewed as an instance of such a framework and (ii) we design a new efficient simulation algorithm that improves the state of the art. 1
Bisimulation and simulation algorithms on probabilistic transition systems by abstract interpretation
"... Abstract We show how bisimulation equivalence and simulation preorder on probabilistic LTSs (PLTSs), namely the main behavioural relations on probabilistic nondeterministic processes, can be characterized by abstract interpretation. Both bisimulation and simulation can be obtained as completions of ..."
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Abstract We show how bisimulation equivalence and simulation preorder on probabilistic LTSs (PLTSs), namely the main behavioural relations on probabilistic nondeterministic processes, can be characterized by abstract interpretation. Both bisimulation and simulation can be obtained as completions of partitions and preorders, viewed as abstract domains, w.r.t. a pair of concrete functions that encode a PLTS. This approach provides a general framework for designing algorithms that compute bisimulation and simulation on PLTSs. Notably, (i) we show that the standard bisimulation algorithm by Baier et al. (2000) can be viewed as an instance of such a framework and (ii) we design a new efficient simulation algorithm that improves the state of the art.
Uniform logical characterizations of testing equivalences for nondeterministic, probabilistic and Markovian processes
 In Proc. of the 7th Int. Workshop on Quantitative Aspects of Programming Languages (QAPL 2009), volume 253(3) of ENTCS
, 2009
"... Logical characterizations of nondeterministic, probabilistic, and Markovian variants of bisimulation equivalence rely on similar modal languages, each including true, negation, conjunction, and diamond. Likewise, logical characterizations of the corresponding variants of trace equivalence rely on s ..."
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Logical characterizations of nondeterministic, probabilistic, and Markovian variants of bisimulation equivalence rely on similar modal languages, each including true, negation, conjunction, and diamond. Likewise, logical characterizations of the corresponding variants of trace equivalence rely on similar modal languages, each including only true and diamond. Unfortunately, this is not the case with the existing logical characterizations of the corresponding variants of testing equivalence, as they are based on different modal languages. In this paper we show that the logical characterizations of testing equivalences for fully nondeterministic processes, fully probabilistic processes, and fully Markovian processes without silent moves can be harmonized by means of a modal language comprising true, disjunction, and diamond.
A Process Algebra Approach to Fuzzy Reasoning
 IFSAEUSFLAT
, 2009
"... Fuzzy systems address the imprecision of the input and output variables, which formally describe notions like “rather warm” or “pretty cold”, while provide a behaviour that depends on fuzzy data. This class of systems are classically represented by means of Fuzzy Inference Systems (FIS), a computin ..."
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Fuzzy systems address the imprecision of the input and output variables, which formally describe notions like “rather warm” or “pretty cold”, while provide a behaviour that depends on fuzzy data. This class of systems are classically represented by means of Fuzzy Inference Systems (FIS), a computing framework based on the concepts of fuzzy ifthen rules and fuzzy reasoning. Even if FIS are largely used, these lack in compositionality. Moreover, the analysis of modeled behaviuors needs complex analytic tools. In this paper we propose a process algebraic approach to specification and analysis of fuzzy behaviours. Indeed, we introduce a Fuzzy variant of CCS (Calculus of Communicating Processes), that permits compositionally describing fuzzy behaviours. Moreover, we also show how standard process algebra formal tools, like modal logics and behavioural equivalences, can be used for supporting fuzzy reasoning.