Book ChapterDOI
Circuit complexity and multiplicative complexity of Boolean functions
Arist Kojevnikov,Alexander S. Kulikov +1 more
- Vol. 6158, pp 239-245
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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) is given.Abstract:
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 different weights to XOR and AND gates.read more
Citations
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Journal Article
An explicit lower bound of 5n - o(n) for Boolean circuits
Kazuo Iwama,Hiroki Morizumi +1 more
TL;DR: The current best lower bound of 4.5n - o(n) for an explicit family of Boolean circuits is improved to 5n- o( n) using the samefamily of Boolean function.
Book ChapterDOI
An elementary proof of a 3n - o(n) lower bound on the circuit complexity of affine dispersers
TL;DR: A very simple proof of a 3n-o(n) lower bound on the circuit complexity (over the full binary basis) of affine dispersers for sublinear dimension is given.
Journal Article
A better-than-3n lower bound for the circuit complexity of an explicit function.
TL;DR: A (3+1/86)n-o(n) lower bound on the size of a Boolean circuits over the full binary basis for an explicitly defined predicate, namely an affine disperser for sublinear dimension is proved.
Proceedings ArticleDOI
A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function
TL;DR: In this article, a lower bound of 3 + 1/86 n-o(n) for the size of an affine disperser for sublinear dimensions was shown. But the lower bound was not satisfied for the full binary basis.
Journal Article
Circuit size lower bounds and #SAT upper bounds through a general framework.
TL;DR: This paper provides a general framework for proving worst/average case lower bounds for circuits and upper bounds for #SAT that is built on ideas of Chen and Kabanets, and shows that many known proofs (of circuit size lower bounds and higher bounds for#SAT) fall into this framework.
References
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Journal ArticleDOI
A 2dvEv- bit distributed algorithm for the directed Euler trail problem
Wen-Huei Chen,Chuan Yi Tang +1 more
TL;DR: The algorithm can be used as a building block for solving other distributed graph problems, and can be slightly modified to run on a strongly-connected diagraph for generating the existent Euler trail or to report that no Euler trails exist.
Journal ArticleDOI
The synthesis of two-terminal switching circuits
TL;DR: A basic part of the general synthesis problem is the design of a two-terminal network with given operating characteristics, and this work shall consider some aspects of this problem.
Book
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
TL;DR: In this paper, the Jacobi model of an elliptic curve and side-channel analysis was used to construct low-density Parity-Check Codes with Two Information Symbols.
Book
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12-16, 2003, Proceedings
TL;DR: This work discusses the construction of Authentication/Secrecy Codes, performance analysis of M-PSK Signal Constellations in Riemannian Varieties, and fast Decomposition of Polynomials with Known Galois Group.
Journal ArticleDOI
A Boolean function requiring 3n network size
TL;DR: Paul (1977) has proved a 2.5 n -lower bound for the network complexity of an explicit Boolean function, but this work modifications the definition of Paul's function slightly and proves a 3 n - lower bound for that function.