Linear-Input Logic

Signed digit addition and related operations with threshold logic

“…Given that symmetric (generalized or not) functions constitute a frequently used class of Boolean functions and because they are expensive to implement in hardware, in terms of area and delay, their implementation with feedforward LTNs has been the subject of numerous theoretical and practical scientific investigations, see, for example, [22], [23], [24], [25], [16], [21].…”

“…The most network-size efficient approach known so far for the depth-P implementation of symmetric Boolean function with TL is the telescopic sum method, introduced by Minick in [23]. The method can be used for the implementation of any Boolean symmetric function and produces depth-P feed-forward LTNs with the size in the order of yn, measured in terms of LTGs, and with linear weight and fan-in values.…”

“…Lemma 1 [23]. Any Boolean symmetric function p s x I Y x P Y F F F Y x n , described as in (4), can be implemented by a two-layer feed-forward LTN with a size complexity measured in terms of LTGs in the order of yn as follows:…”

Hybrid parallel counters - domino and threshold logic

“…The Minnick family of counters [4] are the fastest known TL implementation. We can construct a hybrid 3:2 counter by using this to compute the carry output and domino to compute the sum output, as seen in Figure 1.…”

On Kolmogorov's superpositions and Boolean functions

“…Many results have been obtained for TGs [51]. The first lower bound of on the size of a TGC for "almost all" n-ary BFs (i.e., f : IB "+ IB) was given in [53].…”