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16
Threevalued abstraction for continuoustime markov chains
 In Proceedings of the International Conference on Computer Aided Verification
, 2007
"... Abstract. This paper proposes a novel abstraction technique for continuoustime Markov chains (CTMCs). Our technique fits within the realm of threevalued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that a ..."
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Abstract. This paper proposes a novel abstraction technique for continuoustime Markov chains (CTMCs). Our technique fits within the realm of threevalued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that are readily obtained from general CTMCs, and to abstract transition probabilities by intervals. It is shown that this provides a conservative abstraction for both true and false for a threevalued semantics of the branchingtime logic CSL (Continuous Stochastic Logic). Experiments on an infinitestate CTMC indicate the feasibility of our abstraction technique. 1
Concurrency and Composition in a Stochastic World
, 2012
"... Abstract. We discuss conceptional and foundational aspects of Markov automata [22]. We place this model in the context of continuous and discretetime Markov chains, probabilistic automata and interactive Markov chains, and provide insight into the parallel execution of such models. We further give ..."
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Cited by 12 (3 self)
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Abstract. We discuss conceptional and foundational aspects of Markov automata [22]. We place this model in the context of continuous and discretetime Markov chains, probabilistic automata and interactive Markov chains, and provide insight into the parallel execution of such models. We further give a detailled account of the concept of relations on distributions, and discuss how this can generalise known notions of weak simulation and bisimulation, such as to fuse sequences of internal transitions. 1
Decision Algorithms for Probabilistic Simulations
, 2009
"... Probabilistic phenomena arise in embedded, distributed, networked, biological and security systems, and are accounted for by various probabilistic modeling formalisms based on labelled transition systems. Among the most popular ones are homogeneous discretetime and continuoustime Markov chains (D ..."
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Cited by 9 (3 self)
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Probabilistic phenomena arise in embedded, distributed, networked, biological and security systems, and are accounted for by various probabilistic modeling formalisms based on labelled transition systems. Among the most popular ones are homogeneous discretetime and continuoustime Markov chains (DTMCs and CTMCs) and their extensions with nondeterminism, which we will consider in this thesis. Simulation relations admit comparing the behavior of two models and provide the principal ingredients to perform abstractions of the models while preserving interesting properties. Intuitively, one model simulates another model if it can imitate all of its moves. Simulation preorders are compositional, thus allowing hierarchical verification and decomposition of difficult verification tasks into several subproblems. Recently, variants of simulation relations, such as simulatability and polynomially accurate probabilistic simulations, have been introduced to prove soundness of security protocols. The focus of this thesis lies in decision algorithms for various simulation preorders of probabilistic systems. We propose efficient decision algorithms and provide also experimental comparisons of these algorithms.
BISIMULATION METRICS FOR CONTINUOUS MARKOV DECISION PROCESSES
"... Abstract. In recent years, various metrics have been developed for measuring the behavioural similarity of ..."
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Abstract. In recent years, various metrics have been developed for measuring the behavioural similarity of
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
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 a Uniform Framework for the Definition of Stochastic Process Languages
, 2009
"... In this paper we show how Rate Transition Systems (RT Ss) can be used as a unifying framework for the definition of the semantics of stochastic process algebras. RT Ss facilitate the compositional definition of such semantics exploiting operators on the next state functions which are the functiona ..."
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In this paper we show how Rate Transition Systems (RT Ss) can be used as a unifying framework for the definition of the semantics of stochastic process algebras. RT Ss facilitate the compositional definition of such semantics exploiting operators on the next state functions which are the functional counterpart of classical process algebra operators. We apply this framework to representative fragments of major stochastic process calculi namely TIPP, PEPA and IML and show how they solve the issue of transition multiplicity in a simple and elegant way. We, moreover, show how RT Ss help describing different languages, their differences and their similarities. For each calculus, we also show the formal correspondence between the RT Ss semantics and the standard SOS one.
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
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.
An Algorithm for Probabilistic Alternating Simulation
"... Abstract. In probabilistic game structures, probabilistic alternating simulation (PAsimulation) relations preserve formulas defined in probabilistic alternatingtime temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the large ..."
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Abstract. In probabilistic game structures, probabilistic alternating simulation (PAsimulation) relations preserve formulas defined in probabilistic alternatingtime temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PAsimulation. It is to our knowledge the first such algorithm that works in polynomial time. Our solution extends the generalised coarsest partition problem (GCPP) to a gamebased setting with mixed strategies. The algorithm has higher complexities than those in the literature for nonprobabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions. 1