Abstract
It is known [1] that any serial-parallel contact circuit (π-circuit), realizing a linear Boolean function essentially dependent on n variables, contains not less than n 2 contacts. In the present paper, this bound is strengthened as follows: for each odd n ≥ 5, any such circuit contains not less than n 2 + 3 contacts; and for each even n that is not a power of 2, not less than n 2 + 2 contacts.
This research was partially supported by the Russian Foundation for Fundamental Research (Grant 93–01–16009).
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References
V. M. Khrapchenko (1971) A certain method of obtaining estimates from below for the complexity of π-schemes (in Russian), Mat. Zametki 10, No. 1, 83–92.
S. V. Yablonskiĭ (1954) Realization of a linear function in a class of π-schemes (in Russian), Dokl. Akad. Nauk SSSR 94, No. 5, 805–806.
V. M. Khrapchenko (1971) The complexity of the realization of a linear function in a class of π-schemes (in Russian), Mat. Zametki 9, No. 1, 35–40.
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© 1996 Kluwer Academic Publishers
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Rychkov, K.L. (1996). On the Lower Bounds for the Complexity of Serial-Parallel Contact Circuits Realizing Linear Boolean Functions. In: Korshunov, A.D. (eds) Discrete Analysis and Operations Research. Mathematics and Its Applications, vol 355. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1606-7_16
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DOI: https://doi.org/10.1007/978-94-009-1606-7_16
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