Delay in networks of functional elements in a model with an arbitrary distribution of basis element input delays

Delays of schemes in a model that considers the input values of functional elements

“…In this work, the above relations are extended on the basis of the results in [2] to the main model of SFE delay in basis B; i.e., the following statements are proved:…”

“…Let us consider model M of the delay of SFE over B introduced in [1] and the generalizing model pre sented in [2]. Model M is referred to as main and is related to the auxiliary model M' of type [2] for the delay of SFE over B.…”

“…Model M is referred to as main and is related to the auxiliary model M' of type [2] for the delay of SFE over B. In the main model, for each FE Ᏹ i , 1 ≤ i ≤ b, at any j, 1 ≤ j ≤ k i , and arbitrary Boolean set α, α ∈ (for natural number n, the n fold Cartesian power of set B is denoted by B n ), such that FLA ϕ i (α 1 , …, α j -1 , x j , α j + 1 , …, ) is not constant, positive delay of FE Ᏹ i with respect…”

“…Let us give our definition of the delay of an arbitrary SFE in model M that generalizes the definition of SFE delay in auxiliary model M' [2]. An SFE composed of d series connected FEs is considered a chain of length d, d ≥ 0.…”

“…The main chain ω of SFE Σ is considered to be essential on the set α if ω implements an essential FLA from the separated input of its first functional element, ω being considered an independent scheme whose unseparated inputs are assigned values that approach these inputs on set α in a scheme Σ that contains ω. The set of main chains of SFE Σ that are essential on the set α is denoted by Ω α (Σ As in [2], the rise of branches of FE outputs to the inputs of the scheme in the main model does not change the scheme's delay. As in [3], for each SFE in the main model there is an equivalent formula (sys tem of formulas) in the same basis whose delay is the delay of the initial SFE.…”