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Verifying Temporal Properties of Systems

  • Julian Charles Bradfield

Part of the Progress in Theoretical Computer Science book series (PTCS)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Julian Charles Bradfield
    Pages 1-13
  3. Julian Charles Bradfield
    Pages 14-29
  4. Julian Charles Bradfield
    Pages 30-50
  5. Julian Charles Bradfield
    Pages 51-84
  6. Julian Charles Bradfield
    Pages 85-100
  7. Julian Charles Bradfield
    Pages 101-104
  8. Back Matter
    Pages 105-115

About this book

Introduction

This monograph aims to provide a powerful general-purpose proof tech­ nique for the verification of systems, whether finite or infinite. It extends the idea of finite local model-checking, which was introduced by Stirling and Walker: rather than traversing the entire state space of a model, as is done for model-checking in the sense of Emerson, Clarke et ai. (checking whether a (finite) model satisfies a formula), local model-checking asks whether a particular state satisfies a formula, and only explores the nearby states far enough to answer that question. The technique used was a tableau method, constructing a tableau according to the formula and the local structure of the model. This tableau technique is here generalized to the infinite case by considering sets of states, rather than single states; because the logic used, the propositional modal mu-calculus, separates simple modal and boolean connectives from powerful fix-point operators (which make the logic more expressive than many other temporal logics), it is possible to give a rela­ tively straightforward set of rules for constructing a tableau. Much of the subtlety is removed from the tableau itself, and put into a relation on the state space defined by the tableau-the success of the tableau then depends on the well-foundedness of this relation. The generalized tableau technique is exhibited on Petri nets, and various standard notions from net theory are shown to playa part in the use of the technique on nets-in particular, the invariant calculus has a major role.

Keywords

Finite Invariant calculus logic petri net proof verification

Authors and affiliations

  • Julian Charles Bradfield
    • 1
  1. 1.Department of Computer ScienceUniversity of EdinburghEdinburghUK

Bibliographic information