Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

Assume-guarantee verification for probabilistic systems

We present a compositional verification technique for systems that exhibit both probabilistic and nondeterministic behaviour. We adopt an assume- guarantee approach to verification, where both the assumptions made about system components and the guarantees that they provide are regular safety properties, represented by finite automata. Unlike previous proposals for assume-guarantee reasoning about probabilistic systems, our approach does not require that components interact in a fully synchronous fashion. In addition, the compositional verification method is efficient and fully automated, based on a reduction to the problem of multi-objective probabilistic model checking. We present asymmetric and circular assume-guarantee rules, and show how they can be adapted to form quantitative queries, yielding lower and upper bounds on the actual probabilities that a property is satisfied. Our techniques have been implemented and applied to several large case studies, including instances where conventional probabilistic verification is infeasible

Quantitative multi-objective verification for probabilistic systems

We present a verification framework for analysing multiple quantitative objectives of systems that exhibit both nondeterministic and stochastic behaviour. These systems are modelled as probabilistic automata, enriched with cost or reward structures that capture, for example, energy usage or performance metrics. Quantitative properties of these models are expressed in a specification language that incorporates probabilistic safety and liveness properties, expected total cost or reward, and supports multiple objectives of these types. We propose and implement an efficient verification framework for such properties and then present two distinct applications of it: firstly, controller synthesis subject to multiple quantitative objectives; and, secondly, quantitative compositional verification. The practical applicability of both approaches is illustrated with experimental results from several large case studies

A model checker for performance and dependability properties

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [8] and the continuous time setting [1], [3]. In this short paper, we describe the prototype model checker $E \vdash M C^2$ for discrete and continuous-time Markov chains, where properties are expressed in appropriate extensions of CTL.We illustrate the general benefits of this approach and discuss the structure of the tool