Formal Methods in System Design

, Volume 10, Issue 2–3, pp 171–206 | Cite as

Algebric Decision Diagrams and Their Applications

  • R.I. Bahar
  • E.A. Frohm
  • C.M. Gaona
  • G.D. Hachtel
  • E. Macii
  • A. Pardo
  • F. Somenzi

Abstract

In this paper we present theory and experimental results on Algebraic Decision Diagrams. These diagrams extend BDDs by allowing values from an arbitrary finite domain to be associated with the terminal nodes of the diagram. We present a treatment founded in Boolean algebras and discuss algorithms and results in several areas of application: Matrix multiplication, shortest path algorithms, and direct methods for numerical linear algebra. Although we report an essentially negative result for Gaussian elimination per se, we propose a modified form of ADDs which appears to circumvent the difficulties in some cases. We discuss the relevance of our findings and point to directions for future work.

decision diagrams graph algorithms linear algebra 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • R.I. Bahar
    • 1
  • E.A. Frohm
    • 1
  • C.M. Gaona
    • 1
  • G.D. Hachtel
    • 1
  • E. Macii
    • 1
  • A. Pardo
    • 1
  • F. Somenzi
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of ColoradoBoulder

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