Abstract

The paper considers the problem of checking abstraction between two finite-state fair discrete systems . In automata-theoretic terms this is trace inclusion between two nondeterministic Streett automata. We propose to reduce this problem to an algorithm for checking fair simulation between two generalized Büchi automata. For solving this question we present a new triply nested μ -calculus formula which can be implemented by symbolic methods. We then show that every trace inclusion of this type can be solved by fair simulation, provided we augment the concrete system (the contained automaton) by an appropriate ‘non-constraining’ automaton. This establishes that fair simulation offers a complete method for checking trace inclusion for finite-state systems. We illustrate the feasibility of the approach by algorithmically checking abstraction between finite state systems whose abstraction could only be verified by deductive methods up to now.

Highlights

  • A frequently occurring problem in verification of reactive systems is the problem of abstraction in which we are given a concrete reactivePreprint submitted to Elsevier Science system C and an abstract reactive system A and are asked to check whether A abstracts C, denoted C A

  • For finite state fair discrete systems (FDS) we show that there always exists a non-constraining FDS such that the synchronous composition of this FDS with the concrete system is fairly-simulated by the abstract system

  • The transformation of an FDS to a just discrete system (JDS) follows the transformation of Streett automata to generalized Buchi automata

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Summary

Introduction

A frequently occurring problem in verification of reactive systems is the problem of abstraction (symmetrically refinement) in which we are given a concrete reactive. In the case of generalized Streett[1] games, a deterministic parity automaton for the winning condition has |JC | · |JA| states and index 3, where |JC | and |JA| denote the number of Buchi sets in the fairness of CB and AB respectively. Wishing to apply our algorithm to check the abstraction LATE EARLY, the user has to specify the augmentation of the concrete system by a temporal tester for the LTL formula (x = 2), i.e. a non-constraining FDS that anticipates whether a state marked by 2 is eventually reached or not Using this augmentation, the algorithm manages to prove that the augmented system (LATE +tester) is fairly simulated ( abstracted) by EARLY. A preliminary version of this paper appeared in [16]

The Computational Model
The Open View of a System
Fair Simulation and Simulation Games
Trace Inclusion and Fair Simulation
Closing the Gap
Examples
Experimental Results
A Proof of the Conversion of FDS to JDS

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