Formal verification of an arbiter cascade

  • Hartmann J. Genrich
  • Robert M. Shapiro
Submitted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 616)

Abstract

The asynchronous access of a group of users (e.g. processors) to a single resource (e.g. bus) is regulated by a cascade of arbiters. A single arbiter circuit handles two users. The cascade permits any number of users to be serviced. We use a hierarchical Colored Petri Net to describe the arbiter circuit and the protocol for using it. We also describe the layout of a 2d input cascade of (2d-1) arbiters, d≥1 being the depth of the cascade. We verify the proper functioning of the cascade, first for depth d=1 using an occurrence graph analyzer to prove crucial invariants and confonmance to the protocol; then for arbitrary depth using mathematical induction. As an alternative proof, we develop equivalent Petri net substitutes for the building blocks of the design and verify the resultant special net using classical net theoretic methods. Based on the verification we propose a change of the arbiter to speed-up the cascade.

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References

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    Meta Software Corporation: Design/CPN reference manual. Version 1.75, Aug. 1991Google Scholar
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    Meta Software Corporation: The Design/CPN occurrence graph analyzer. Version 0.2, Dec. 1991Google Scholar
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    Huber, P.; Jensen, A.M.; Jepsen, L.O.; Jensen, K.: Reachability trees for high-level Petri nets. Theoretical Computer Science 45 (1986), 261–292CrossRefGoogle Scholar
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    Valmari, Antti: Stubborn sets for reduced state space generation. In: Advances in Petri Nets 1990 (G. Rozenberg, Ed.), Lecture Notes in Computer Science 483, Berlin: Springer-Verlag (1991)Google Scholar
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    Varshavsky, Victor I.: Circuits insensitive to delays in transistors and wires. Helsinki University of Technology, Digital Systems Laboratory (November 1989)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Hartmann J. Genrich
    • 1
  • Robert M. Shapiro
    • 2
  1. 1.Gesellschaft für Mathematik und DatenverarbeitungSankt Augustin 1Germany
  2. 2.Meta Software CorporationCambridgeUSA

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