We consider concurrent probabilistic systems, based on probabilistic automata of Segala & Lynch [55], which allow non-deterministic choice between probability distributions. These systems can be decomposed into a collection of "computation trees" which arise by resolving the non-deterministic, but not probabilistic, choices. The presence of non-determinism means that certain liveness properties cannot be established unless fairness is assumed. We introduce a probabilistic branching time logic PBTL, based on the logic TPCTL of Hansson [30] and the logic PCTL of [55], resp. pCTL of [14]. The formulas of the logic express properties such as "every request is eventually granted with probability at least p". We give three interpretations for PBTL on concurrent probabilistic processes: the first is standard, while in the remaining two interpretations the branching time quantifiers are taken to range over a certain kind of fair computation trees. We then present a model checking algorithm for...

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This paper deals with probabilistic and nondeterministic processes represented by a variant of labelled transition systems where any outgoing transition of a state s is augmented with probabilities for the possible successor states. Our main contribution are algorithms for computing the bisimulation equivalence classes as introduced by Larsen & Skou [44] and the simulation preorder `a la Segala & Lynch [57]. The algorithm for deciding bisimilarity is based on a variant of the traditional partitioning technique [43, 51] and runs in time O(mn(log m+ log n)) where m is the number of transitions and n the number of states. The main idea for computing the simulation preorder is the reduction to maximum flow problems in suitable networks. Using the method of Cheriyan, Hagerup & Mehlhorn [15] for computing the maximum flow, the algorithm runs in time O((mn 6 +m 2 n 3 )= log n). Moreover, we show that the network-based technique is also applicable to compute the simulation-like relation...

Abstract. Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace

This paper presents a mu-calculus-based modal logic for describing properties of probabilistic labeled transition systems (PLTSs) and develops a model-checking algorithm for determining whether or not states in finite-state PTLSs satisfy formulas in the logic. The logic is based on the distinction between (probabilistic) "systems" and (non-probabilistic) "observations": using the modal mu-calculus, one may specify sets of observations, and the semantics of our logic then enable statements to be made about the measures of such sets at various system states. The logic may be used to encode a variety of probabilistic modal and temporal logics; in addition, the model-checking problem for it may be reduced to the calculation of solutions to systems of non-linear equations. 1 Introduction Classical temporal-logic model checking [CES86, McM93] provides a basis for automatically checking the correctness of finite-state systems such as hardware designs and communication protocols. In this fram...

This paper provides an elementary introduction to the probabilistic automaton (PA) model, which has been developed by Segala. We describe how distributed systems with discrete probabilities can be modeled and analyzed by means of PAs. We explain how the basic concepts for the analysis of nonprobabilistic automata can be extended to probabilistic systems. In particular, we treat the parallel composition operator on PAs, the semantics of a PA as a set of trace distributions, an extension of the PA model with time and simulation relations for PAs. Finally, we give an overview of various other state based models that are used for the analysis of probabilistic systems.

Abstract. Probabilistic automata (PAs) constitute a general framework for modeling and analyzing discrete event systems that exhibit both nondeterministic and probabilistic behavior, such as distributed algorithms and network protocols. The behavior of PAs is commonly defined using schedulers (also called adversaries or strategies), which resolve all nondeterministic choices based on past history. From the resulting purely probabilistic structures, trace distributions can be extracted, whose intent is to capture the observable behavior of a PA. However, when PAs are composed via an (asynchronous) parallel composition operator, a global scheduler may establish strong correlations between the behavior of system components and, for example, resolve nondeterministic choices in one PA based on the outcome of probabilistic choices in the other. It is well known that, as a result of this, the (linear-time) trace distribution precongruence is not compositional for PAs. In his 1995 Ph.D. thesis, Segala has shown that the (branching-time) probabilistic simulation preorder is compositional for PAs. In this paper, we establish that the simulation preorder is, in fact, the coarsest refinement of the trace distribution preorder that is compositional. We prove our characterization result by providing (1) a context of a given PA A, called the tester, which may announce the state of A to the outside world, and (2) a specific global scheduler, called the observer, which ensures that the state information that is announced is actually correct. Now when another PA B is composed with the tester, it may generate the same external behavior as the observer only when it is able to simulate A in the sense that whenever A goes to some state s, B can go to a corresponding state u, from which it may generate the same external behavior. Our result shows that probabilistic contexts together with global schedulers are able to exhibit the branching structure of PAs.

In this paper we present an algebraic language for the specification of probabilistic and nondeterministic processes, PNAL, which is a probabilistic extension of EPL (Algebraic Theory of Processes, M. Hennessy) that maintains nondeterminism.

In this paper we introduce a new approach to the formal design and modelling of QoS parameters in multimedia systems. This approach is based on the principle of separation of concerns. We use the process algebra based language LOTOS to specify the functional behaviour of the system and separately describe the quality of service requirements using an appropriate temporal logic. This temporal logic integrates real-time and stochastic constructs to enable the expression of QoS parameters such as deadlines, jitter and error rates. The specifications are then linked together in the same model. We also define a mapping from temporal logic statements to event schedulers. These schedulers can then be used to monitor the events that occur in the system and ensure that the system's behaviour achieves the QoS requirements. 1 Introduction Over the past few years a wide range of distributed systems has emerged to support multimedia applications. These systems are characterized by the processing an...

In this paper we present a new approach to the formal specification of distributed real-time systems using the formal description technique LOTOS together with a real-time temporal logic SQTL. This approach characterized by a separation of concerns, aims to construct abstractly a model from the a functional specification according to real-time constraints. The functional behaviour is described in LOTOS without regard for the time critical constraints. The specification is then extended with precise real-time properties written in SQTL. We present a method to generate a timing event scheduler from the properties in order to monitor the functional behaviour. The model of event schedulers is based on timed automata and intended to be used for an automata-based verification technique. 1 Introduction Over the past few years there have been several formal techniques used for the design and verification of distributed systems. The most popular ones are process algebras, Petri nets and finit...