Results 1  10
of
32
Automated Verification Techniques for Probabilistic Systems
"... Abstract. This tutorial provides an introduction to probabilistic model checking, a technique for automatically verifying quantitative properties of probabilistic systems. We focus on Markov decision processes (MDPs), which model both stochastic and nondeterministic behaviour. We describe methods to ..."
Abstract

Cited by 40 (17 self)
 Add to MetaCart
(Show Context)
Abstract. This tutorial provides an introduction to probabilistic model checking, a technique for automatically verifying quantitative properties of probabilistic systems. We focus on Markov decision processes (MDPs), which model both stochastic and nondeterministic behaviour. We describe methods to analyse a wide range of their properties, including specifications in the temporal logics PCTL and LTL, probabilistic safety properties and cost or rewardbased measures. We also discuss multiobjective probabilistic model checking, used to analyse tradeoffs between several different quantitative properties. Applications of the techniques in this tutorial include performance and dependability analysis of networked systems, communication protocols and randomised distributed algorithms. Since such systems often comprise several components operating in parallel, we also cover techniques for compositional modelling and verification of multicomponent probabilistic systems. Finally, we describe three large case studies which illustrate practical applications of the various methods discussed in the tutorial. 1
Logical Characterizations of Bisimulations for Discrete Probabilistic Systems
, 2007
"... We give logical characterizations of bisimulation relations for the probabilistic automata of Segala in terms of three HennessyMilner style logics. The three logics characterize strong, strong probabilistic and weak probabilistic bisimulation, and differ only for the kind of diamond operator used. ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
(Show Context)
We give logical characterizations of bisimulation relations for the probabilistic automata of Segala in terms of three HennessyMilner style logics. The three logics characterize strong, strong probabilistic and weak probabilistic bisimulation, and differ only for the kind of diamond operator used. Compared to the Larsen and Skou logic for reactive systems, these logics introduce a new operator that measures the probability of the set of states that satisfy a formula. Moreover, the satisfaction relation is defined on measures rather than single states. We rederive previous results of Desharnais et. al. by defining sublogics for Reactive and Alternating Models viewed as restrictions of probabilistic automata. Finally, we identify restrictions on probabilistic automata, weaker than those imposed by the Alternating Models, that preserve the logical characterization of Desharnais et. al. These restrictions require that each state either enables several ordinary transitions or enables a single probabilistic transition.
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 ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
(Show Context)
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
Scalar outcomes suffice for finitary probabilistic testing
 of Lecture Notes in Computer Science
, 2007
"... Abstract. The question of equivalence has long vexed research in concurrency, leading to many different denotational and bisimulationbased approaches; a breakthrough occurred with the insight that tests expressed within the concurrent framework itself, based on a special “success action”, yield ..."
Abstract

Cited by 18 (11 self)
 Add to MetaCart
(Show Context)
Abstract. The question of equivalence has long vexed research in concurrency, leading to many different denotational and bisimulationbased approaches; a breakthrough occurred with the insight that tests expressed within the concurrent framework itself, based on a special “success action”, yield equivalences that make only inarguable distinctions. When probability was added, however, it seemed necessary to extend the testing framework beyond a direct probabilistic generalisation in order to remain useful. An attractive possibility was the extension to multiple success actions that yielded vectors of realvalued outcomes. Here we prove that such vectors are unnecessary when processes are finitary, that is finitely branching and finitestate: single scalar outcomes are just as powerful. Thus for finitary processes we can retain the original, simpler testing approach and its direct connections to other naturally scalarvalued phenomena. 1
Weak Bisimulation for Probabilistic Timed Automata
 PROC. OF SEFM’03, IEEE CS
, 2003
"... We are interested in describing timed systems that exhibit probabilistic behaviour. To this purpose, we consider a model of Probabilistic Timed Automata and introduce a concept of weak bisimulation for these automata, together with an algorithm to decide it. The weak bisimulation relation is shown t ..."
Abstract

Cited by 17 (6 self)
 Add to MetaCart
We are interested in describing timed systems that exhibit probabilistic behaviour. To this purpose, we consider a model of Probabilistic Timed Automata and introduce a concept of weak bisimulation for these automata, together with an algorithm to decide it. The weak bisimulation relation is shown to be preserved when either time, or probability are abstracted away. As an application, we use weak bisimulation for Probabilistic Timed Automata to model and analyze a timing attack on the dining cryptographers protocol.
Branching cells as local states for event structures and nets: Probabilistic applications
 In Proceedings of 8th FoSSaCS, volume 3441 of LNCS
, 2005
"... Abstract. We study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is ..."
Abstract

Cited by 15 (9 self)
 Add to MetaCart
(Show Context)
Abstract. We study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is to bring an interpretation of branching cells as a right notion of “local state”, for concurrent systems. We illustrate the above claim through applications to probabilistic concurrent models. In this respect, our results extends in part previous work by VaraccaVölzerWinskel on probabilistic confusion free event structures. We propose a construction for probabilities over socalled locally finite event structures that makes concurrent processes probabilistically independent—simply attach a dice to each branching cell; dices attached to concurrent branching cells are thrown independently. Furthermore, we provide a true concurrency generalization of Markov chains, called Markov nets. Unlike in existing variants of stochastic Petri nets, our approach randomizes Mazurkiewicz traces, not firing sequences. We show in this context the Law of Large Numbers (LLN), which confirms that branching cells deserve the status of local state. Our study was motivated by the stochastic modeling of fault propagation and alarm correlation in telecommunications networks and services. It provides the foundations for probabilistic diagnosis, as well as the statistical distributed learning of such models. 1
Flow faster: Efficient decision algorithms for probabilistic simulations
 13th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS), volume 4424 of LNCS
"... Abstract. Strong and weak simulation relations have been proposed for Markov chains, while strong simulation and strong probabilistic simulation relations have been proposed for probabilistic automata. However, decision algorithms for strong and weak simulation over Markov chains, and for strong sim ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
(Show Context)
Abstract. Strong and weak simulation relations have been proposed for Markov chains, while strong simulation and strong probabilistic simulation relations have been proposed for probabilistic automata. However, decision algorithms for strong and weak simulation over Markov chains, and for strong simulation over probabilistic automata are not efficient, which makes it as yet unclear whether they can be used as effectively as their nonprobabilistic counterparts. This paper presents drastically improved algorithms to decide whether some (discrete or continuoustime) Markov chain strongly or weakly simulates another, or whether a probabilistic automaton strongly simulates another. The key innovation is the use of parametric maximum flow techniques to amortize computations. We also present a novel algorithm for deciding strong probabilistic simulation preorders on probabilistic automata, which has polynomial complexity via a reduction to an LP problem. When extending the algorithms for probabilistic automata to their continuoustime counterpart, we retain the same complexity for both strong and strong probabilistic simulations.
Branching bisimulation for probabilistic systems: characteristics and decidability
 Theoretical Computer Science
"... We address the concept of abstraction in the setting of probabilistic reactive systems, and study its formal underpinnings for the strictly alternating model of Hansson. In particular, we define the notion of branching bisimilarity and study its properties by studying two other equivalence relations ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
(Show Context)
We address the concept of abstraction in the setting of probabilistic reactive systems, and study its formal underpinnings for the strictly alternating model of Hansson. In particular, we define the notion of branching bisimilarity and study its properties by studying two other equivalence relations, viz. coloured trace equivalence and branching bisimilarity using maximal probabilities. We show that both alternatives coincide with branching bisimilarity. The alternative characterisations have their own merits and focus on different aspects of branching bisimilarity. Coloured trace equivalence can be understood without knowledge of probability theory and is independent of the notion of a scheduler. Branching bisimilarity, rephrased in terms of maximal probabilities gives rise to an algorithm of polynomial complexity for deciding the equivalence. Together they give a better understanding of branching bisimilarity. Furthermore, we show that the notions of branching bisimilarity in the alternating model of Hansson and in the nonalternating model of Segala differ: branching bisimilarity in the latter setting turns out to discriminate between systems that are intuitively branching bisimilar. 1
Axiomatization of trace semantics for stochastic nondeterministic processes. Quantitative Evaluation of Systems
 In Proceedings of QEST
, 2004
"... We give a complete axiomatization of trace distribution precongruence for probabilistic nondeterministic processes based on a process algebra that includes internal behavior and recursion. The axiomatization is given for two different semantics of the process algebra that are consistent with the alt ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
We give a complete axiomatization of trace distribution precongruence for probabilistic nondeterministic processes based on a process algebra that includes internal behavior and recursion. The axiomatization is given for two different semantics of the process algebra that are consistent with the alternating model of Hansson and the nonalternating model of Segala, respectively. It is shown that the two semantics coincide up to trace distribution precongruence. 1.