Summary
We characterize the optimal networks for a simultaneous computation of AND and NOR over the base of all 16 Boolean operators. We show that the optimal networks for AND and NOR are precisely the networks that consist of a disjoint union of an optimal network for AND with an optimal network for NOR.
Similar content being viewed by others
References
Paul, W.: A 2.5n lower bound on the combinatorial complexity of Boolean functions. SIAM J. Comput. 6, 427–443 (1977)
Paul, W.: Realizing Boolean functions on disjoint sets of variables. Theor. Comp. Sci. 2, 383–396 (1976)
Pippenger, N., Fischer, M.J.: Relation among complexity measures. JACM 26, 361–381 (1979)
Savage, J.E.: Computional work and time on finite machines. JACM 19, 660–674 (1972)
Schnorr, C.P.: The network complexity and the Turing machine complexity of finite functions. Acta Informat. 7, 95–107 (1976)
Schnorr, C.P.: The combinatorial complexity of equivalence. Theor. Comp. Sci. 1, 289–295 (1976)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Blum, N., Seysen, M. Characterization of all optimal networks for a simultaneous computation of AND and NOR. Acta Informatica 21, 171–181 (1984). https://doi.org/10.1007/BF00289238
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00289238