On the Existence of Hazard-Free Multi-Level Logic

  • Authors:
  • Steven M. Nowick;Charles W. O 'Donnell

  • Affiliations:
  • -;-

  • Venue:
  • ASYNC '03 Proceedings of the 9th International Symposium on Asynchronous Circuits and Systems
  • Year:
  • 2003

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Abstract

This paper introduces a new method which, given an arbitrary Boolean function and specified set of (function hazard-free) input transitions, determines if any hazard-free multi-level logic implementation exists. The algorithm is based on iterative decomposition, sing disjunction and inversion.Earlier approaches by Nowick/Dill [7] and Theobald/Nowick [8] have been proposed to determine if a hazard-free two-level logic implementation exists. However, it is well-known that the effects of multi-level transformations are quite complex: since they can both decrease and increase logic hazards in a given circuit. In this paper, a method is proposed to solve the hazard-free multi-level existence problem. The method is proven to be both sound and complete for a large class of multi-level implementations. A novel contribution is to show that, if any hazard-free multi-level solution exists, then a hazard-free solution always exists using only 3 logic levels, in a 3-level NAND or OR-AND-OR structure. Moreover, in this case, it is shown there always exists a unique canonical hazard-free 3-level implementation.