Abstract
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.
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References
Lamagna & Savage: Combinational Complexity of Some Monotone Functions, 15 th SWAT Conference, 1974
Mehlhorn: On the Complexity of Monotone Realizations of Matrix Multiplication, Univ.d. Saarlandes, TR 74-11, Sept. 1974
Paterson: Complexity of Monotone Network for Boolean Matrix Product, Univ. of Warwick, TR 2, July 1974.
Pratt: The Power of Negative Thinking in Multiplying Boolean Matrices, 6 th SIGACT Conference, 1974.
Schnorr: Lower Bounds on the Complexity of Monotone Networks, unpublished memo.
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© 1975 Springer-Verlag Berlin Heidelberg
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Mehlhorn, K., Galil, Z. (1975). Monotone switching circuits and boolean matrix product. In: Bečvář, J. (eds) Mathematical Foundations of Computer Science 1975 4th Symposium, Mariánské Lázně, September 1–5, 1975. MFCS 1975. Lecture Notes in Computer Science, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07389-2_214
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DOI: https://doi.org/10.1007/3-540-07389-2_214
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