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

A Monte Carlo model checker for probabilistic LTL with numerical constraints

We define the syntax and semantics of a new temporal logic called probabilistic LTL with numerical constraints (PLTLc). We introduce an efficient model checker for PLTLc properties. The efficiency of the model checker is through approximation using Monte Carlo sampling of finite paths through the model’s state space (simulation outputs) and parallel model checking of the paths. Our model checking method can be applied to any model producing quantitative output – continuous or stochastic, including those with complex dynamics and those with an infinite state space. Furthermore, our offline approach allows the analysis of observed (real-life) behaviour traces. We find in this paper that PLTLc properties with constraints over free variables can replace full model checking experiments, resulting in a significant gain in efficiency. This overcomes one disadvantage of model checking experiments which is that the complexity depends on system granularity and number of variables, and quickly becomes infeasible. We focus on models of biochemical networks, and specifically in this paper on intracellular signalling pathways; however our method can be applied to a wide range of biological as well as technical systems and their models. Our work contributes to the emerging field of synthetic biology by proposing a rigourous approach for the structured formal engineering of biological systems

Control of Probabilistic Systems under Dynamic, Partially Known Environments with Temporal Logic Specifications

We consider the synthesis of control policies for probabilistic systems, modeled by Markov decision processes, operating in partially known environments with temporal logic specifications. The environment is modeled by a set of Markov chains. Each Markov chain describes the behavior of the environment in each mode. The mode of the environment, however, is not known to the system. Two control objectives are considered: maximizing the expected probability and maximizing the worst-case probability that the system satisfies a given specification

Quantitative Verification: Formal Guarantees for Timeliness, Reliability and Performance

Computerised systems appear in almost all aspects of our daily lives, often in safety-critical scenarios such as embedded control systems in cars and aircraft or medical devices such as pacemakers and sensors. We are thus increasingly reliant on these systems working correctly, despite often operating in unpredictable or unreliable environments. Designers of such devices need ways to guarantee that they will operate in a reliable and efficient manner. Quantitative verification is a technique for analysing quantitative aspects of a system's design, such as timeliness, reliability or performance. It applies formal methods, based on a rigorous analysis of a mathematical model of the system, to automatically prove certain precisely specified properties, e.g. ``the airbag will always deploy within 20 milliseconds after a crash'' or ``the probability of both sensors failing simultaneously is less than 0.001''. The ability to formally guarantee quantitative properties of this kind is beneficial across a wide range of application domains. For example, in safety-critical systems, it may be essential to establish credible bounds on the probability with which certain failures or combinations of failures can occur. In embedded control systems, it is often important to comply with strict constraints on timing or resources. More generally, being able to derive guarantees on precisely specified levels of performance or efficiency is a valuable tool in the design of, for example, wireless networking protocols, robotic systems or power management algorithms, to name but a few. This report gives a short introduction to quantitative verification, focusing in particular on a widely used technique called model checking, and its generalisation to the analysis of quantitative aspects of a system such as timing, probabilistic behaviour or resource usage. The intended audience is industrial designers and developers of systems such as those highlighted above who could benefit from the application of quantitative verification,but lack expertise in formal verification or modelling