Delay-Insensitivity and Semi-Modularity

  • Authors:
  • J. A. Brzozowski;H. Zhang

  • Affiliations:
  • Department of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1. brzozo@uwaterloo.ca;Department of Computer Science, University of Toronto, Toronto, ON, Canada M5S 3G4. richard@dgp.utoronto.ca

  • Venue:
  • Formal Methods in System Design
  • Year:
  • 2000

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Abstract

The study of asynchronous circuit behaviors in the presenceof component and wire delays has received a great deal of attention.In this paper, we consider asynchronous circuits whose components canbe any non-deterministic sequential machines of the Moore type, anddescribe a formal model for these circuits and their behaviors underthe inertial delay model.We model an asynchronous circuit C by a networkN of modules with delaysassociated with its components and/or wires. We compute the behavior ofNassuming arbitrary inertial delays in the modules, and take this behavior tobe correct. We define N to be strongly delay-insensitive ifits behavior remains correct in the presence of arbitrary stray delays,where correctness is defined through the notion of observational equivalence(or bisimulation), one of the strongest forms of behavioral equivalence. Weintroduce the notion of quasi semi-modularity, which generalizesMuller's definitionof semi-modularity to non-deterministic networks. We prove that a circuit,with all the wire delays taken into account, isstrongly delay-intensitive if and only if its behavior is quasisemi-modular.