Abstract not found

Symbolic model checking for purely probabilistic processes using MTBDDs [12] was introduced in [4] and further developed in [20, 3]. In this paper we consider models for concurrent probabilistic systems similar to those of [28, 7, 5] and the concurrent Markov chains of [35, 13], which extend the purely probabilistic processes through the addition of nondeterministic choice. As a specification formalism we use the probabilistic branching-time temporal logic PBTL of [5, 7], which allows us to express properties such as "under any scheduling of nondeterministic choices, the probability of OE holding until / is true is at least 0.78". In [5, 7] it is shown that the verification of "until" properties can be reduced to a linear programming problem and solved with the help of e.g. the simplex algorithm, but no symbolic model checking is considered. Based on the algorithms of [5, 7], we derive symbolic model checking procedure for PBTL over concurrent probabilistic systems using MTBDDs, and extend it with fairness constraints. We furthermore implement an experimental model checker using the Colorado University Decision Diagram (CUDD) package [32]. Our key contribution is an implementation of the simplex algorithm in terms of MTBDDs.

We study various notions of probabilistic bisimulation from a coalgebraic point of view, accumulating in a hierarchy of probabilistic system types. In general, a natural transformation between two Set-functors straightforwardly gives rise to a transformation of coalgebras for the respective functors. This latter transformation preserves homomorphisms and thus bisimulations. For comparison of probabilistic system types we also need reflection of bisimulation. We build the hierarchy of probabilistic systems by exploiting the new result that the transformation also reflects bisimulation in case the natural transformation is componentwise injective and the first functor preserves weak pullbacks. Additionally, we illustrate the correspondence of concrete and coalgebraic bisimulation in the case of general Segala-type systems.

) P. R. D'Argenio 1 , J.-P. Katoen 2 , and E. Brinksma 1 1 Dept. of Computer Science. University of Twente. P.O.Box 217. 7500 AE Enschede. The Netherlands. fdargenio,brinksmag@cs.utwente.nl 2 Lehrstuhl fur Informatik VII. University of Erlangen-Nurnberg. Martensstrasse 3. D-91058 Erlangen. Germany. katoen@informatik.uni-erlangen.de Abstract We introduce a framework to study stochastic systems, i.e. systems in which the time of occurrence of activities is a general random variable. We introduce and discuss in depth a stochastic process algebra (named ) adequate to specify and analyse those systems. In order to give semantics to , we also introduce a model that is an extension of traditional automata with clocks which are basically random variables: the stochastic automata model. We show that this model and are equally expressive. Although stochastic automata are adequate to analyse systems since they are finite objects, they are still too coarse to serve as concrete semantic...

A Markov decision process is a generalization of a Markov chain in which both probabilistic and nondeterministic choice coexist. Given a Markov decision process with costs associated with the transitions and a set of target states, the stochastic shortest path problem consists in computing the minimum expected cost of a control strategy that guarantees to reach the target. In this paper, we consider the classes of stochastic shortest path problems in which the costs are all non-negative, or all non-positive. Previously, these two classes of problems could be solved only under the assumption that the policies that minimize or maximize the expected cost also lead to the target with probability 1. This assumption does not necessarily hold for Markov decision processes that arise as model for distributed probabilistic systems. We present efficient methods for solving these two classes of problems without relying on additional assumptions. The methods are based on algorithms to transform th...

. Traditional methods for the analysis of system performance and reliability generally assume a precise knowledge of the system and its workload. Here, we present methods that are suited for the analysis of systems that contain partly unknown or unspecified components, such as systems in their early design stages. We introduce stochastic transition systems, a high-level formalism for the modeling of timed probabilistic systems. Stochastic transition systems extend current modeling capabilities by enabling the representation of transitions having unknown delay distributions, alongside transitions with zero or exponentially-distributed delay. We show how these various types of transitions can be uniformly represented in terms of nondeterminism, probability, fairness and time, yielding efficient algorithms for system analysis. Finally, we present methods for the specification and verification of long-run average properties of STSs. These properties include many relevant performance and re...

Abstract. We present MC 2, what we believe to be the first randomized, Monte Carlo algorithm for temporal-logic model checking, the classical problem of deciding whether or not a property specified in temporal logic holds of a system specification. Given a specification S of a finite-state system, an LTL (Linear Temporal Logic) formula ϕ, and parameters ɛ and δ, MC 2 takes N = ln(δ) / ln(1 − ɛ) random samples (random walks ending in a cycle, i.e lassos) from the Büchi automaton B = BS × B¬ϕ to decide if L(B) = ∅. Should a sample reveal an accepting lasso l, MC 2 returns false with l as a witness. Otherwise, it returns true and reports that with probability less than δ, pZ < ɛ, where pZ is the expectation of an accepting lasso in B. It does so in time O(N · D) and space O(D), where D is B’s recurrence diameter, using a number of samples N that is optimal to within a constant factor. Our experimental results demonstrate that MC 2 is fast, memory-efficient, and scales very well.

This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [BDEP97]. The thrust of that work was an extension of the notion of bisimulation to systems with continuous state spaces; for example for systems where the state space is the real numbers. In the present paper we study the logical characterization of probabilistic bisimulation for such general systems. This study revealed some unexpected results even for discrete probabilistic systems. ffl Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be characterized by several inequivalent logics; we report five in this paper. ffl We do not need any finite branching assumption yet there is no need of infinitary conjunction. ffl The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts abou...

The increasing dependence of businesses on distributed architectures and computer networking places heavy demands on the speed and reliability of data exchange, leading to the emergence of sophisticated protocols which involve both real-time and randomization, for example FireWire IEEE1394. Automatic verification techniques such as model checking have been adapted to this class of probabilistic, timed systems [1, 9, 3, 14]. This abstract considers an application of such techniques to the IEEE1394 (FireWire) root contention protocol, in which the interplay between timed and probabilistic aspects is used to break the symmetry which may arise during the leader election process. Here, the properties of interest concern the election of a leader within a certain deadline, with a certain probability or greater. Our specification formalism is that of probabilistic timed automata [14], a variant of timed automa...

This paper investigates probability in the presence of causal dependence. More precisely, it studies the process model of probabilistic event structures. In their simplest form probabilistic choice is localised to cells at which immediate conflict arises; in which case probabilistic independence coincides with causal independence. An event structure is associated with a domain—that of its configurations ordered by inclusion. In domain theory probabilistic processes are denoted by continuous valuations on a domain. A key result of this paper is a representation theorem showing how continuous valuations on the domain of a confusion free event structure correspond to the probabilistic event structures it supports. Via a notion of tests, probabilistic event structures are related to another approach to probabilistic processes, viz. Markov decision processes. Tests and morphisms of event structures point the way to a more general theory in which, for example, event structures need not be confusion free. 1