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Comparative branchingtime semantics for Markov chains
 Information and Computation
, 2003
"... This paper presents various semantics in the branchingtime spectrum of discretetime and continuoustime Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilisti ..."
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Cited by 64 (17 self)
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This paper presents various semantics in the branchingtime spectrum of discretetime and continuoustime Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilistic Computation Tree Logic) and CSL (Continuous Stochastic Logic). Apart from presenting various existing branchingtime relations in a uniform manner, this paper presents the following new results: (i) strong simulation for CTMCs, (ii) weak simulation for CTMCs and DTMCs, (iii) logical characterizations thereof (including weak bisimulation for DTMCs), (iv) a relation between weak bisimulation and weak simulation equivalence, and (v) various connections between equivalences and preorders in the continuous and discretetime setting. The results are summarized in a branchingtime spectrum for DTMCs and CTMCs elucidating their semantics as well as their relationship. Key Words: comparative semantics, Markov chain, (weak) simulation, (weak) bisimulation, temporal logic
Probability and Nondeterminism in Operational Models of Concurrency
 In Proc. CONCUR, LNCS
, 2006
"... Abstract. We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analy ..."
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Cited by 19 (1 self)
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Abstract. We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analysis of randomized distributed 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 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.
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.
Deciding Probabilistic Automata Weak Bisimulation in Polynomial Time
"... Deciding in an efficient way weak probabilistic bisimulation in the context of probabilistic automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step cond ..."
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Cited by 4 (2 self)
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Deciding in an efficient way weak probabilistic bisimulation in the context of probabilistic automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step condition of the bisimulation. This enables us to arrive at a polynomial time algorithm for deciding weak probabilistic bisimulation. We also present several extensions to interesting related problems setting the ground for the development of more effective and compositional analysis algorithms for probabilistic systems.
New Results on Abstract Probabilistic Automata
, 2011
"... Probabilistic Automata (PAs) are a recognized framework for modeling and analysis of nondeterministic systems Probabilistic Automata (APAs)—an abstraction framework for PAs. In this paper, we discuss APAs over dissimilar alphabets, a determinisation operator, conjunction of nondeterministic APAs, a ..."
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Cited by 1 (1 self)
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Probabilistic Automata (PAs) are a recognized framework for modeling and analysis of nondeterministic systems Probabilistic Automata (APAs)—an abstraction framework for PAs. In this paper, we discuss APAs over dissimilar alphabets, a determinisation operator, conjunction of nondeterministic APAs, and an APAembedding of Interface Automata. We conclude introducing a tool for automatic manipulation of APAs.
REVISITING TRACE AND TESTING EQUIVALENCES FOR NONDETERMINISTIC AND PROBABILISTIC PROCESSES
, 2013
"... Vol. 10(1:16)2014, pp. 1–42 www.lmcsonline.org ..."
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Specification Theories for Probabilistic and RealTime Systems
"... Abstract. We survey extensions of modal transition systems to specification theories for probabilistic and timed systems. 1 ..."
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Abstract. We survey extensions of modal transition systems to specification theories for probabilistic and timed systems. 1