Monotone switching circuits and boolean matrix product

Extended Abstract
  • Kurt Mehlhorn
  • Zvi Galil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 32)


We explore the concept of local transformations of monotone switching circuits, i.e. what kind of local changes in a circuit leave the functions computed by the circuit invariant. We obtain several general theorems in this direction. We apply these results to boolean matrix product and prove that the school-method for matrix multiplication yields the unique monotone circuit.


Local Change Transformation Rule General Theorem Negative Thinking Injective Mapping 
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  1. Lamagna & Savage: Combinational Complexity of Some Monotone Functions, 15 th SWAT Conference, 1974Google Scholar
  2. Mehlhorn: On the Complexity of Monotone Realizations of Matrix Multiplication, Univ.d. Saarlandes, TR 74-11, Sept. 1974Google Scholar
  3. Paterson: Complexity of Monotone Network for Boolean Matrix Product, Univ. of Warwick, TR 2, July 1974.Google Scholar
  4. Pratt: The Power of Negative Thinking in Multiplying Boolean Matrices, 6 th SIGACT Conference, 1974.Google Scholar
  5. Schnorr: Lower Bounds on the Complexity of Monotone Networks, unpublished memo.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  • Zvi Galil
    • 2
    • 1
  1. 1.Universität des Saarlandes 66SaarbrückenWest - Germany
  2. 2.Dept. of Computer ScienceCornell UniversityIthacaU. S. A.

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