Linear temporal logic and z refinement

Since Z, being a state-based language, describes a system in terms of its state and potential state changes, it is natural to want to describe properties of a specified system also in terms of its state. One means of doing this is to use Linear Temporal Logic (LTL) in which properties about the state of a system over time can be captured. This, however, raises the question of whether these properties are preserved under refinement. Refinement is observation preserving and the state of a specified system is regarded as internal and, hence, non-observable. In this paper, we investigate this issue by addressing the following questions. Given that a Z specification A is refined by a Z specification C, and that P is a temporal logic property which holds for A, what temporal logic property Q can we deduce holds for C? Furthermore, under what circumstances does the property Q preserve the intended meaning of the property P? The paper answers these questions for LTL, but the approach could also be applied to other temporal logics over states such as CTL and the mgr-calculus.

Verifying data refinements using a model checker

In this paper, we consider how refinements between state-based specifications (e.g., written in Z) can be checked by use of a model checker. Specifically, we are interested in the verification of downward and upward simulations which are the standard approach to verifying refinements in state-based notations. We show how downward and upward simulations can be checked using existing temporal logic model checkers. In particular, we show how the branching time temporal logic CTL can be used to encode the standard simulation conditions. We do this for both a blocking, or guarded, interpretation of operations (often used when specifying reactive systems) as well as the more common non-blocking interpretation of operations used in many state-based specification languages (for modelling sequential systems). The approach is general enough to use with any state-based specification language, and we illustrate how refinements between Z specifications can be checked using the SAL CTL model checker using a small example.

Model checking Z specifications using SAL

The Symbolic Analysis Laboratory (SAL) is a suite of tools for analysis of state transition systems. Tools supported include a simulator and four temporal logic model checkers. The common input language to these tools was originally developed with translation from other languages, both programming and specification languages, in mind. It is, therefore, a rich language supporting a range of type definitions and expressions. In this paper, we investigate the translation of Z specifications into the SAL language as a means of providing model checking support for Z. This is facilitated by a library of SAL definitions encoding the Z mathematical toolkit.

Formal analysis of human-computer interaction using model checking

Experiments with simulators allow psychologists to better understand the causes of human errors and build models of cognitive processes to be used in human reliability assessment (HRA). This paper investigates an approach to task failure analysis based on patterns of behaviour, by contrast to more traditional event-based approaches. It considers, as a case study, a formal model of an air traffic control (ATC) system which incorporates controller behaviour. The cognitive model is formalised in the CSP process algebra. Patterns of behaviour are expressed as temporal logic properties. Then a model-checking technique is used to verify whether the decomposition of the operator's behaviour into patterns is sound and complete with respect to the cognitive model. The decomposition is shown to be incomplete and a new behavioural pattern is identified, which appears to have been overlooked in the analysis of the data provided by the experiments with the simulator. This illustrates how formal analysis of operator models can yield fresh insights into how failures may arise in interactive systems.

An automated failure mode and effect analysis based on high-level design specificication with behavior trees

Formal methods have significant benefits for developing safety critical systems, in that they allow for correctness proofs, model checking safety and liveness properties, deadlock checking, etc. However, formal methods do not scale very well and demand specialist skills, when developing real-world systems. For these reasons, development and analysis of large-scale safety critical systems will require effective integration of formal and informal methods. In this paper, we use such an integrative approach to automate Failure Modes and Effects Analysis (FMEA), a widely used system safety analysis technique, using a high-level graphical modelling notation (Behavior Trees) and model checking. We inject component failure modes into the Behavior Trees and translate the resulting Behavior Trees to SAL code. This enables us to model check if the system in the presence of these faults satisfies its safety properties, specified by temporal logic formulas. The benefit of this process is tool support that automates the tedious and error-prone aspects of FMEA.

Compositional verification for object-Z

This paper presents a framework for compositional verification of Object-Z specifications. Its key feature is a proof rule based on decomposition of hierarchical Object-Z models. For each component in the hierarchy local properties are proven in a single proof step. However, we do not consider components in isolation. Instead, components are envisaged in the context of the referencing super-component and proof steps involve assumptions on properties of the sub-components. The framework is defined for Linear Temporal Logic (LTL)