ABSTRACT

Upper and lower bounds are derived for the number of pseudothreshold functions of n variables. (Pseudothershold logic is a generalization of threshold logic.) It is shown that a lower bound on the number of pseudothreshold functions P(n) of exactly n variables realized by zero-free structures is The number of pseudothreshold functions Q(n) of n variables realized by nontrivial structures is bounded by It is also proven that is a lower bound on the number of positive functions of exactly n variables.

INDEX TERMS

Bounds, positive functions, pseudothreshold functions, separable functions, threshold functions, threshold logic.

CITATION

C. Baugh, "Bounds on the Number of Pseudothreshold Functions," in

*IEEE Transactions on Computers*, vol. 20, no. , pp. 1602-1605, 1971.

doi:10.1109/T-C.1971.223181

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