Temporal Properties Of Systems Research Articles

An Interval Temporal Logic for Time Series Specification and Data Integration

The analysis of temporal series—in particular, analysis of multisensor data—is a complex problem. It depends on the application domain, the way the data have to be used, and sensors available, among other factors. Various models, algorithms, and technologies have been designed for this goal. Temporal logics are used to describe temporal properties of systems. The properties may specify the occurrence and the order of events in time, recurring patterns, complex behaviors, and processes. In this paper, a new interval logic, called duration calculus for functions (DC4F), is proposed for the specification of temporal series corresponding to multisensor data. DC4F is a natural extension of the well-known duration calculus, an interval temporal logic for the specification of process duration. The adequacy of the proposed logic is analyzed in the case of multisensor data concerning volcanic eruption monitoring. It turns out that the relevant behavior concerns time intervals, not only accumulated history as it is described in other kinds of temporal logics. The examples analyzed demonstrate that a description language is required to specify time series of various kind relative to time intervals. The duration calculus cannot be successfully applied for this task. The proposed calculus allows one to specify temporal series and complex interval-dependent behaviors, and to evaluate the corresponding data within a unifying logical framework. It allows to formulate hypotheses concerning volcano eruption phenomena. However, the expressivity of DC4F comes at the cost of its decidability.

Fluctuations and noise-limited sensing near the exceptional point of parity-time-symmetric resonator systems

We theoretically explore the role of mesoscopic fluctuations and noise on the spectral and temporal properties of systems of $\mathcal{PT}$-symmetric coupled gain-loss resonators operating near the exceptional point, where eigenvalues and eigenvectors coalesce. We show that the inevitable detuning in the frequencies of the uncoupled resonators leads to an unavoidable modification of the conditions for reaching the exceptional point, while, as this point is approached in ensembles of resonator pairs, statistical averaging significantly smears the spectral features. We also discuss how these fluctuations affect the sensitivity of sensors based on coupled $\mathcal{PT}$-symmetric resonators. Finally, we show that temporal fluctuations in the detuning and gain of these sensors lead to a quadratic growth of the optical power in time, thus implying that maintaining operation at the exceptional point over a long period can be rather challenging. Our theoretical analysis clarifies issues central to the realization of $\mathcal{PT}$-symmetric devices, and should facilitate future experimental work in the field.

Verifying Temporal Properties of Reactive Systems by Transformation

We show how program transformation techniques can be used for the verification of both safety and liveness properties of reactive systems. In particular, we show how the program transformation technique distillation can be used to transform reactive systems specified in a functional language into a simplified form that can subsequently be analysed to verify temporal properties of the systems. Example systems which are intended to model mutual exclusion are analysed using these techniques with respect to both safety (mutual exclusion) and liveness (non-starvation), with the errors they contain being correctly identified.

Temporal stabilizability and compensatability of time-varying linear discrete-time systems with white stochastic parameters

This paper reveals that apart from changes of system structure vital system properties such as stabilizability and compensatability may be lost temporarily due to the stochastic nature of system parameters. To that end new system properties called temporal mean-square stabilizability (tms-stabilizability) and temporal mean-square compensatability (tms-compensatability) for time-varying linear discrete-time systems with white stochastic parameters (multiplicative white noise) are developed. When controlling such systems by means of (optimal) state feedback, tms-stabilizability identifies intervals where mean-square stability (ms-stability) is lost temporarily. This is vital knowledge to both control engineers and system scientists. Similarly, tms-compensatability identifies intervals where ms-stability is lost temporarily in case of full-order (optimal) output feedback. Tests explicit in the system matrices are provided to determine each temporal system property. These tests compute measures of the associated temporal system properties. Relations among the new system properties as well as relations with associated existing system properties are investigated and established. Examples illustrating principal applications and practical importance are provided.

Model-based test generation using extended symbolic grammars

A novel, model-based test case generation approach for validating reactive systems, especially those supporting richly structured data inputs and/or interactions, is presented. Given an executable system model and an extended symbolic grammar specifying plausible system inputs, the approach performs a model-based simulation to (i) ensure the consistency of the model with respect to the specified inputs, and (ii) generate corresponding test cases for validating the system. The model-based simulation produces a state transition diagram (STD) automatically justifying the model runtime behaviors within the test case coverage. The STD can further be transformed to produce an evolved symbolic grammar, which can then be used to incrementally generate a refined set of test cases. As a case study, we present a live sequence chart (LSC) model-based test generator, named LCT in short, for LSC simulation and consistency testing. The evolved symbolic grammar produced by the simulator can either be used to generate practical test cases for software testing, or be further refined by applying our model-based test generation approach again with additional test coverage criteria. We further show that LSCs can also be used to specify and test certain temporal system properties during the model simulation. Their satisfaction, reflected in the STD, can either be served as a directive for selective test generation, or a basis for further temporal property model checking.

Model checking processes specified in join-calculus algebra

This article presents a model checking tool used to verify concurrent systems specified in join-calculus algebra. The temporal properties of systems under verification are expressed in CTL logic. Join-calculus algebra with its operational semantics defined by the chemical abstract machine serves as the basic method for the specification of concurrent systems and their synchronization mechanisms, and allows the examination of more complex systems.

Theoretical and numerical issues concerning temporal stabilisability and detectability

Motivated by the design of perturbation (output) feedback controllers for nonlinear systems, temporal system properties have been developed by the authors, for time-varying linear continuous-time systems. In particular temporal controllability/reachability, temporal stabilisability, temporal reconstructability/observability and temporal detectability. As opposed to their ordinary counterparts, these temporal properties identify the temporal loss of stabilisability and detectability that may occur for time-varying linear continuous-time systems obtained e.g. by linearising around state and control trajectories of a non-linear system. One contribution of this paper is to show that temporal stabilisability and temporal detectability require a measure of state decay that cannot be independent of the state representation and state vector norm. This raises the issue of how to select the state representation or norm. The second contribution of this paper is to deal with this selection. Thirdly this paper presents two new, alternative ways to compute temporal stabilisability and detectability and their associated measures. They are compared with computations proposed earlier that rely on LQ control. Finally, through simple illustrative examples, numerical aspects concerning computation of temporal stabilisability and detectability and their associated measures are investigated.

Visual Specifications for Temporal Reasoning

Graphical interval logic (GIL) is a visual temporal logic in which formulas resemble the informal timing diagrams familiar to system designers and software engineers. It provides an intuitive and natural visual notation in which to express specifications for concurrent systems and retains the benefits of a formal notation. A visual editor permits GIL specifications to be easily constructed, and to be stored in and retrieved from files. The editor interfaces with a proof checker and model generator, which permit verification of temporal inferences. The paper shows how graphical specifications are created and used to reason about temporal properties of systems. It shows how pictures that formalize temporal arguments enhance understanding and help motivate successful proof strategies.

Book Review: Verifying Temporal Properties of Systems, by Julian Charles Bradfield

Book Review: Verifying Temporal Properties of Systems, by Julian Charles Bradfield

Specification and verification of decentralized daisy chain arbiters with ω-extended regular expressions

We introduce ω-extended regular expressions (ωEREs) that can be used for specifying and proving properties of the set of finite of infinite event sequences that occur in a system. The ability of ωEREs to deal with infinite as well as finite sequences allows us to specify and verify eventuality and liveness properties quite naturally. ωEREs have a number of operators similar to those found in temporal logic and they are suitable for expressing temporal properties of systems. The problem of verifying properties of a system can be formulated as the containment problem for two ωEREs which is solvable. The use of ωEREs for specification and verification is illustrated with an example of a class of logical circuits called ‘decentralized daisy chain arbiters’ that are used for arbitrating between the requests issued by a number of concurrent processes.