this paper we present a breadth-rst search style algorithm which enables practical implementation of the resolution method for temporal logics developed by Fisher [15]. Fisher's method has been shown correct [36], deals with the full range of past and futuretime temporal operators and has only one temporal resolution rule making it suitable for mechanisation. The resolution procedure is characterised by translation to a normal form, the application of a classical style resolution rule to derive contradictions that occur at the same point in time (termed step resolution), together with a new resolution rule, which derives contradictions over temporal sequences (termed temporal resolution). As it is the latter that is the most expensive part of the algorithm, involving search through graphs, as well as the most novel, it is on the application of the temporal resolution rule that we concentrate. We suggest a breadth-rst search approach to the application of the temporal resolution rule and through analysis of its operation and output, explain why it is an improvement on search mechanisms suggested previously [12]

. We propose a modular approach to the formal specication of the requirements on embedded systems. In this approach, requirements on data are specied as invariants on states. Requirements on behaviour are specied assertionally by temporal logic formulae, restricting the runs of the system. The proposed method is modular, because components can be specied and analysed in isolation, and the views of several components can be combined in an easy way. Requirements can be combined by simply putting them in conjunction. A mathematical framework supporting this approach is developed and implemented in the theorem prover PVS. The method is illustrated by formalising the requirements of a miniature embedded system. This specication is then analysed using the theorem prover, revealing some errors in the original specication. Keywords: formal requirements specication, embedded systems, modularity, data and behaviour, states and events, linear temporal logic, PVS. 1 Introduction The requir...

This chapter discusses propositional and rst-order temporal logic of programs with time corresponding to integers. The logic contains past and future temporal operators. We concentrate mainly on the formal verification of temporal properties. A variety of proof systems is presented in both Hilbert and Gentzen styles. Various notions of soundness and completeness are investigated. We also discuss applications of the logic in the formal speci cation and verification of properties of algorithms and data structures.