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- Schnorr: Lower Bounds on the Complexity of Monotone Networks, unpublished memo.Google Scholar