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45
Stochastic transition systems for continuous state spaces and nondeterminism
 In FoSSaCS’05, LNCS 3441
, 2005
"... Abstract. We study the interaction between nondeterministic and probabilistic behaviour in systems with continuous state spaces, arbitrary probability distributions and uncountable branching. Models of such systems have been proposed previously. Here, we introduce a model that extends probabilistic ..."
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Cited by 17 (4 self)
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Abstract. We study the interaction between nondeterministic and probabilistic behaviour in systems with continuous state spaces, arbitrary probability distributions and uncountable branching. Models of such systems have been proposed previously. Here, we introduce a model that extends probabilistic automata to the continuous setting. We identify the class of schedulers that ensures measurability properties on executions, and show that such measurability properties are preserved by parallel composition. Finally, we demonstrate how these results allow us to define an alternative notion of weak bisimulation in our model. 1
Tutte le algebre insieme: Concepts, discussions and relations of stochastic process algebras with general distributions
 In Validation of Stochastic Systems
, 2004
"... Abstract. We report on the state of the art in the formal specification and analysis of concurrent systems whose activity duration depends on general probability distributions. First of all the basic notions and results introduced in the literature are explained and, on this basis, a conceptual clas ..."
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Cited by 15 (3 self)
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Abstract. We report on the state of the art in the formal specification and analysis of concurrent systems whose activity duration depends on general probability distributions. First of all the basic notions and results introduced in the literature are explained and, on this basis, a conceptual classification of the different approaches is presented. We observe that most of the approaches agree on the fact that the specification of systems with general distributions has a three level structure: the process algebra level, the level of symbolic semantics and the level of concrete semantics. Based on such observations, a new very expressive model is introduced for representing timed systems with general distributions. We show that many of the approaches in the literature can be mapped into this model establishing therefore a formal framework to compare these approaches. 1
S.: A characterization of meaningful schedulers for continuoustime Markov decision processes. In: Formal Modeling and Analysis of Timed Systems
 LNCS
, 2006
"... Abstract. Continuoustime Markov decision process are an important variant of labelled transition systems having nondeterminism through labels and stochasticity through exponential firetime distributions. Nondeterministic choices are resolved using the notion of a scheduler. In this paper we chara ..."
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Cited by 14 (1 self)
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Abstract. Continuoustime Markov decision process are an important variant of labelled transition systems having nondeterminism through labels and stochasticity through exponential firetime distributions. Nondeterministic choices are resolved using the notion of a scheduler. In this paper we characterize the class of measurable schedulers, which is the most general one, and show how a measurable scheduler induces a unique probability measure on the sigmaalgebra of infinite paths. We then give evidence that for particular reachability properties it is sufficient to consider a subset of measurable schedulers. Having analyzed schedulers and their induced probability measures we finally show that each probability measure on the sigmaalgebra of infinite paths is indeed induced by a measurable scheduler which proves that this class is complete. 1
Symbolic Computation of Maximal Probabilistic Reachability
 In Proc. CONCUR'01, volume 2154 of LNCS
, 2001
"... We study the maximal reachability probability problem for infinitestate systems featuring both nondeterministic and probabilistic choice. The problem involves the computation of the maximal probability of reaching a given set of states, and underlies decision procedures for the automatic verificati ..."
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Cited by 12 (8 self)
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We study the maximal reachability probability problem for infinitestate systems featuring both nondeterministic and probabilistic choice. The problem involves the computation of the maximal probability of reaching a given set of states, and underlies decision procedures for the automatic verification of probabilistic systems. We extend the framework of symbolic transition systems, which equips an infinitestate system with an algebra of symbolic operators on its state space, with a symbolic encoding of probabilistic transitions to obtain a model for an infinitestate probabilistic system called a symbolic probabilistic system.
Bounded Model Checking for GSMP Models of Stochastic Realtime Systems
 In Proc. of HSCC’06, LNCS 3927
, 2006
"... Model checking is a popular algorithmic verification technique for checking temporal requirements of mathematical models of systems. In this paper, we consider the problem of verifying bounded reachability properties of stochastic realtime systems modeled as generalized semiMarkov processes (GS ..."
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Cited by 11 (1 self)
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Model checking is a popular algorithmic verification technique for checking temporal requirements of mathematical models of systems. In this paper, we consider the problem of verifying bounded reachability properties of stochastic realtime systems modeled as generalized semiMarkov processes (GSMP).
Extending PDDL to Model Stochastic Decision Processes
, 2003
"... We present an extension of PDDL for modeling stochastic decision processes. Our domain description language allows the specification of actions with probabilistic effects, exogenous events, and actions and events with delayed effects. The result is a language that can be used to specify stochast ..."
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Cited by 9 (0 self)
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We present an extension of PDDL for modeling stochastic decision processes. Our domain description language allows the specification of actions with probabilistic effects, exogenous events, and actions and events with delayed effects. The result is a language that can be used to specify stochastic decision processes, both discretetime and continuoustime, of varying complexity. We also propose the use of established logic formalisms, taken from the model checking community, for specifying probabilistic temporally extended goals.
On ZoneBased Analysis of Duration Probabilistic Automata
"... We propose an extension of the zonebased algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than settheoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continu ..."
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Cited by 8 (2 self)
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We propose an extension of the zonebased algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than settheoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuouslydistributed durations. For this model we develop an extension of the zonebased forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the boundedhorizon behavior of cyclic DPA). 1
P.R.: General distributions in process algebra. In: Lectures on formal methods and performance analysis: first EEF/Euro summer school on trends in computer science
, 2002
"... Abstract. This paper is an informal tutorial on stochastic process algebras, i.e., process calculi where action occurrences may be subject to a delay that is governed by a (mostly continuous) random variable. Whereas most stochastic process algebras consider delays determined by negative exponenti ..."
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Cited by 8 (1 self)
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Abstract. This paper is an informal tutorial on stochastic process algebras, i.e., process calculi where action occurrences may be subject to a delay that is governed by a (mostly continuous) random variable. Whereas most stochastic process algebras consider delays determined by negative exponential distributions, this tutorial is concerned with the integration of general, nonexponential distributions into a process algebraic setting. We discuss the issue of incorporating such distributions in an interleaving semantics, and present some existing solutions to this problem. In particular, we present a process algebra for the specification of stochastic discreteevent systems modeled as generalized semiMarkov chains (GSMCs). Using this language stochastic discreteevent systems can be described in an abstract and modular way. The operational semantics of this process algebra is given in terms of stochastic automata, a novel mixture of timed automata and GSMCs. We show that GSMCs are a proper subset of stochastic automata, discuss various notions of equivalence, present congruence results, treat equational reasoning, and argue how an expansion law in the process algebra can be obtained. As a case study, we specify the root contention phase within the standardized IEEE 1394 serial bus protocol and study the delay until root contention resolution. An overview of related work on general distributions in process algebra and a discussion of trends and future work complete this tutorial. 1
Probabilistic Timed Behavior Trees
"... Abstract The Behavior Tree notation has been developed as a method for systematically and traceably capturing user requirements. In this paper we extend the notation with probabilistic behaviour, so that reliability, performance, and other dependability properties can be expressed. The semantics of ..."
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Cited by 5 (2 self)
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Abstract The Behavior Tree notation has been developed as a method for systematically and traceably capturing user requirements. In this paper we extend the notation with probabilistic behaviour, so that reliability, performance, and other dependability properties can be expressed. The semantics of probabilistic timed Behavior Trees is given by mapping them to probabilistic timed automata. We gain advantages for requirements capture using Behavior Trees by incorporating into the notation an existing elegant specification formalism (probabilistic timed automata) which has tool support for formal analysis of probabilistic user requirements.
Almostsure modelchecking of reactive timed automata
 In QEST’12
, 2012
"... Abstract—We consider the model of stochastic timed automata, a model in which both delays and discrete choices are made probabilistically. We are interested in the almostsure modelchecking problem, which asks whether the automaton satisfies a given property with probability 1. While this problem wa ..."
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Cited by 4 (0 self)
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Abstract—We consider the model of stochastic timed automata, a model in which both delays and discrete choices are made probabilistically. We are interested in the almostsure modelchecking problem, which asks whether the automaton satisfies a given property with probability 1. While this problem was shown decidable for singleclock automata few years ago, it was also proven that the algorithm for this decidability result could not be used for general timed automata. In this paper we describe the subclass of reactive timed automata, and we prove decidability of the almostsure modelchecking problem under that restriction. Decidability relies on the fact that this model is almostsurely fair. As a desirable property of real systems, we show that reactive automata are almostsurely nonZeno. Finally we show that the almostsure modelchecking problem can be decided for specifications given as deterministic timed automata. I.