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A tree search algorithm for low multiplicative complexity logic design

Future Generation Computer Systems, 2018
Low multiplicative complexity logic design is a useful heuristic to achieve low gate count implementation of logic circuit. In this work, we propose a deterministic approach based on the currently known lower and upper bounds of multiplicative complexity
Ming Ming Wong
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On the Multiplicative Complexity of Boolean Functions

Fundamenta Informaticae, 2016
The multiplicative complexity μ(f) of a Boolean function f is the smallest number of & (of AND gates) in circuits in the basis {x&y, x⊕y, 1} such that each circuit implements the function f. By μ(S) we denote the number of & (of AND gates) in a circuit S in the basis {x&y, x ⊕ y, 1}. We present a method to construct circuits in the basis {x&y, x ⊕ y, 1}
S. Selezneva
openaire   +2 more sources

Circuit Complexity and Multiplicative Complexity of Boolean Functions

Conference on Computability in Europe, 2010
In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 - c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key idea of the proof is a circuit complexity measure assigning
Arist Kojevnikov, Alexander S. Kulikov
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Multiplicative complexity of vector valued Boolean functions [PDF]

Theoretical Computer Science, 2018
We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called ΣΠΣ circuits, we show that there is a
Joan Boyar
exaly   +2 more sources

On multiplicative complexity of computing polynomials

Proceedings of Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications", 2022
The paper estimates the multiplicative complexity of computing the class complex polynomials in n variables of degree d. At constant d the order of complexity is set - the new one is the lower bound for odd d.
I. Sergeev
semanticscholar   +1 more source

The multiplicative complexity of boolean functions

International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 1989
Let the multiplicative complexity L(f) of a boolean function f be the minimal number of Λ-gates (with two entries) that are sufficient to evaluate f by circuits over the basis Λ,⊕,1. We relate L(f) with the dimension of the dual domain D(f); D(f) is the minimal linear space of linear boolean forms such that f modulo linear functions can be written as a
C. Schnorr
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Multiplicative complexity of bijective 4×4 S-boxes

Cryptography and Communications, 2014
Pavol Zajac, Zajac Pavol
exaly   +2 more sources

On the multiplicative complexity of some Boolean functions

Computational Mathematics and Mathematical Physics, 2015
S N Selezneva, Selezneva S N
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Duhamel/Hollmann-Like Discrete Fourier Transform Algorithm With the Smallest Multiplicative Complexity Over a Finite Field

IEEE Transactions on Signal Processing, 2020
The new method for the discrete Fourier transform computation over a finite field is introduced. This method is a nontrivial generalization of the Duhamel–Hollmann algorithm with replacement of the Toeplitz convolution calculation by the normalized ...
S. Fedorenko
semanticscholar   +1 more source

Low multiplicative complexity logic minimisation over the basis (AND, XOR, NOT)

Electronics Letters, 2016
M L Dennis Wong
exaly   +2 more sources