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Error in the UNITY substitution rule for subscripted operators

Published: 01 July 1994 Publication History

Abstract

UNITY, introduced by Chandy and Misra [ChM88], is a programming logic intended to reason about temporal properties of distributed programs. Despite the fact that UNITY does not have the full power of, for example, linear temporal logic, it enjoys popularity due to its simplicity.
There was however a serious problem with the Substitution Rule. The logic is incomplete without the rule, and with the rule it is inconsistent.
Latterly Beverly Sanders introduced the concept of strongest invariant and proposed a new definition for UNITY [San91] that fixes the problem with the Substitution Rule. For the benefit of program union, she also introduced the concept of subscripted properties and claimed a generalized version of Substitution Rule for the subscripted properties.
This report presents an example that shows that the latter claim is false. A proposal as how to fix this follows.

References

References

[1]
Chandy, K. M. and Misra, J.:Parallel Program Design, a Foundation. Addison-Wesley, 1988.
[2]
Sanders B. A. Eliminating the Substitution Axiom from UNITY Logic Formal Aspects of Computing 1991 3 189-205
[3]
Misra, J.:Soundness of the Substitution Axiom. Notes on UNITY: 14–90.

Cited By

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  • (2006)Compositionality for Tightly Coupled SystemsElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2005.12.073159(299-323)Online publication date: 1-May-2006
  • (2005)A UNITY-Based Framework Towards Component Based SystemsPrinciples of Distributed Systems10.1007/11516798_4(52-66)Online publication date: 23-Aug-2005

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Published In

cover image Formal Aspects of Computing
Formal Aspects of Computing  Volume 6, Issue 4
Jul 1994
112 pages
ISSN:0934-5043
EISSN:1433-299X
Issue’s Table of Contents

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 July 1994
Accepted: 15 December 1993
Received: 15 December 1993
Published in FAC Volume 6, Issue 4

Author Tags

  1. Distributed programming
  2. UNITY
  3. Substitution Rule in UNITY

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Cited By

View all
  • (2006)Compositionality for Tightly Coupled SystemsElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2005.12.073159(299-323)Online publication date: 1-May-2006
  • (2005)A UNITY-Based Framework Towards Component Based SystemsPrinciples of Distributed Systems10.1007/11516798_4(52-66)Online publication date: 23-Aug-2005

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