Claus Thrane

Quantitative analysis of weighted transition systems

Abstract We present a general framework for the analysis of quantitative and qualitative properties of reactive systems, based on a notion of weighted transition systems. We introduce and analyze three different types of distances on weighted transition systems, both in a linear and a branching version. Our quantitative notions appear to be reasonable extensions of the standard qualitative concepts, and the three different types introduced are shown to measure inequivalent properties. When applied to the formalism of weighted timed automata, we show that some standard decidability and undecidability results for timed automata extend to our quantitative setting.

Quantitative refinement for weighted modal transition systems

Specification theories as a tool in the development process of component-based software systems have recently attracted a considerable attention. Current specification theories are however qualitative in nature and hence fragile and unsuited for modern software systems. We propose the first specification theory which allows to capture quantitative aspects during the refinement and implementation process.

Timed automata can always be made implementable

Timed automata follow a mathematical semantics, which assumes perfect precision and synchrony of clocks. Since this hypothesis does not hold in digital systems, properties proven formally on a timed automaton may be lost at implementation. In order to ensure implementability, several approaches have been considered, corresponding to different hypotheses on the implementation platform. We address two of these: A timed automaton is samplable if its semantics is preserved under a discretization of time; it is robust if its semantics is preserved when all timing constraints are relaxed by some small positive parameter. We propose a construction which makes timed automata implementable in the above sense: From any timed automaton A, we build a timed automaton A′ that exhibits the same behaviour as A, and moreover A′ is both robust and samplable by construction.

Metrics for weighted transition systems: Axiomatization and complexity

Abstract Simulation distances are essentially approximations of simulation which provide a measure of the extent by which behaviors in systems are inequivalent. In this paper, we consider the general quantitative model of weighted transition systems, where transitions are labeled with elements of a finite metric space. We study the so-called point-wise and accumulating simulation distances which provide extensions to the well-known Boolean notion of simulation on labeled transition systems. We introduce weighted process algebras for finite and regular behavior and offer sound and (approximate) complete inference systems for the proposed simulation distances. We also settle the algorithmic complexity of computing the simulation distances.

Distances for Weighted Transition Systems: Games and Properties

We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrar y distance on system traces, we show how this leads to natural definitions of a linear and a branching d istance on states of such a transition system. We show that our framework generalizes and unifies a l arge variety of previously considered system distances, and we develop some general properties of our distances. We also show that if the trace distance admits a recursive characterization, then t he corresponding branching distance can be obtained as a least fixed point to a similar recursive charact erization. The central tool in our work is a theory of infinite path-building games with quantitative o bjectives.

Weighted modal transition systems

Specification theories as a tool in model-driven development processes of component-based software systems have recently attracted a considerable attention. Current specification theories are however qualitative in nature, and therefore fragile in the sense that the inevitable approximation of systems by models, combined with the fundamental unpredictability of hardware platforms, makes it difficult to transfer conclusions about the behavior, based on models, to the actual system. Hence this approach is arguably unsuited for modern software systems. We propose here the first specification theory which allows to capture quantitative aspects during the refinement and implementation process, thus leveraging the problems of the qualitative setting.Our proposed quantitative specification framework uses weighted modal transition systems as a formal model of specifications. These are labeled transition systems with the additional feature that they can model optional behavior which may or may not be implemented by the system. Satisfaction and refinement is lifted from the well-known qualitative to our quantitative setting, by introducing a notion of distances between weighted modal transition systems. We show that quantitative versions of parallel composition as well as quotient (the dual to parallel composition) inherit the properties from the Boolean setting.

General quantitative specification theories with modalities

This paper proposes a new theory of quantitative specifications. It generalizes the notions of step-wise refinement and compositional design operations from the Boolean to an arbitrary quantitative setting. It is shown that this general approach permits to recast many existing problems which arise in system design.

Verification, performance analysis and controller synthesis for real-time systems

This article aims at providing a concise and precise Travellers Guide, Phrase Book or Reference Manual to the timed automata modeling formalism introduced by Alur and Dill [7,8]. The paper gives comprehensive definitions of timed automata, priced (or weighted) timed automata, and timed games and highlights a number of results on associated decision problems related to model checking, equivalence checking, optimal scheduling, and the existence of winning strategies.

Slicing for uppaal

This article presents slicing for the model checking tool UPPAAL [1]. Slicing is a technique based on static analysis used to reduce the syntactic size of models or applications. In this article, we show that slicing may be used to construct reachability preserving reductions of UPPAAL models, possibly improving the performance of the tool. We present experiments further validating our claims.

The quantitative linear-time–branching-time spectrum

We present a distance-agnostic approach to quantitative verification. Taking as input an unspecified distance on system traces, or executions, we develop a game-based framework which allows us to define a spectrum of different interesting system distances corresponding to the given trace distance. Thus we extend the classic linear-time--branching-time spectrum to a quantitative setting, parametrized by trace distance. We also provide fixed-point characterizations of all system distances, and we prove a general transfer principle which allows us to transfer counterexamples from the qualitative to the quantitative setting,showing that all system distances are mutually topologically inequivalent.