Automated verification is a technique for establishing if certain properties, usually expressed in temporal logic, hold for a system model. The model can be defined using a high-level formalism or extracted directly from software using methods such as abstract interpretation. The verification proceeds through exhaustive exploration of the state-transition graph of the model and is therefore more powerful than testing. Quantitative verification is an analogous technique for establishing quantitative properties of a system model, such as the probability of battery power dropping below minimum, the expected time for message delivery and the expected number of messages lost before protocol termination. Models analysed through this method are typically variants of Markov chains, annotated with costs and rewards that describe resources and their usage during execution. Properties are expressed in temporal logic extended with probabilistic and reward operators. Quantitative verification involves a combination of a traversal of the state-transition graph of the model and numerical computation. This paper gives a brief overview of current research in quantitative verification, concentrating on the potential of the method and outlining future challenges. The modelling approach is described and the usefulness of the methodology illustrated with an example of a real-world protocol standard – Bluetooth device discovery – that has been analysed using the PRISM model checker (www.prismmodelchecker.org).

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.

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 discrete-time and continuous-time, of varying complexity. We also propose the use of established logic formalisms, taken from the model checking community, for specifying probabilistic temporally extended goals.

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 real-time systems modeled as generalized semi-Markov processes (GSMP).

Abstract. This paper describes work in progess performed as part of an ongoing project aimed at the development of theoretical foundations and model checking algorithms for the verification of soft deadlines in timed systems, that is, properties such as “there is a 90 % chance that the message will be delivered within 5 time units”. The research is focussed on the probabilistic timed automata model [11], an extension of timed automata [3], and includes: model checking of discrete-probabilistic automata based on the region graph construction [11]; symbolic methods based on forwards and backwards reachability [10,13]; and the continuous probabilistic timed automata [12]. 1

We propose probabilistic rewrite theories as a general semantic framework supporting highlevel specification of probabilistic systems that can be massively concurrent. We give the definition and semantics of probabilistic rewrite theories and discuss the mappings between di#erent classes of theories and models. We then define the semantics of probabilistic temporal formulae for a given probabilistic rewrite theory. We explain how real-time probabilistic systems whose time is discrete can be expressed as probabilistic rewrite theories without any extension. Finally we give our design ideas for PMaude, an implementation of probabilistic rewrite theories on top of Maude 2.0. We shall report a running prototype of PMaude in the final version of the paper.

We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuously-distributed durations. For this model we develop an extension of the zone-based 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

this document is its second year report.

Probabilistic model checking is a method for automatically verifying that a probabilistic system satisfies a property with a given likelihood, with the probabilistic temporal logic Pctl being a common choice for the property specification language. In this paper, we explore methods for model checking Pctl properties of infinite-state systems in which probabilistic and nondeterministic behaviour coexist. Building on previous work on computing the maximum probability with which a state set is reached in such systems, we utilize symbolic operations on the state sets to generate a finite-state version of the system on which the Pctl model checking problem can be answered. As in the non-probabilistic case, our model checking algorithm is semi-decidable for infinite-state systems. We illustrate our technique using the formalism of probabilistic timed automata, for which previous Pctl model checking techniques were based on an unnecessarily ne subdivisions of the state space.

... systems featuring both nondeterministic and probabilistic choice. In an earlier paper we de ned symbolic probabilistic systems, an extension of the framework of symbolic transition systems due to Henzinger et. al., and considered the problem of deciding the maximal probability of reaching a set of target states. A symbolic probabilistic system is an in nite-state system equipped with an algebra of symbolic operators on its state space, additionally extended with a symbolic encoding of probabilistic transitions to obtain a model for in nite-state probabilistic systems. In this paper we generalise the notion of symbolic probabilistic systems and consider the minimal reachability problem, that is, the problem of computing the minimal probability of reaching a given set of target states. An exact answer to this problem is obtained algorithmically via iteration of a re ned version of the classical predecessor operation, combined with intersection and set dierence operations. As in the previous work on symbolic transition systems, our state space exploration algorithm is semi-decidable for in nite-state systems. Together with the earlier work concerning the maximal reachability problem, the results presented here yield a semi-decidable algorithm for model checking symbolic systems against the probabilistic temporal logic PCTL. We illustrate our approach with the help of probabilistic timed automata, for which previous veri cation techniques suffered from an unnecessarily ne subdivisions of the state space, or which returned only estimates of the actual probabilities.