Result: The monotone circuit complexity of quadratic boolean functions

Title:
The monotone circuit complexity of quadratic boolean functions
Authors:
AMANO, Kazuyuki, MARUOKA, Akira
Source:
Annual International Symposium on Algorithms and ComputationAlgorithmica. 46(1):3-14
Publisher Information:
New York, NY: Springer, 2006.
Publication Year:
2006
Physical Description:
print, 26 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Complexité calcul, Computational complexity, Complejidad computación, Fonction booléenne, Boolean function, Función booliana, Fonction quadratique, Quadratic function, Función cuadrática, Logique booléenne, Boolean logic, Lógica booleana, Porte logique, Logic gate, Puerta lógica, Théorie graphe, Graph theory, Teoría grafo, Complexité conjonctive, Boolean circuit, Conjunctive complexity, Monotone circuit, Quadratic functions
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Computer Science, Gunma University, Tenjin 1-5-1, Kiryu, Gunma 376-8515, Japan
Graduate School of Information Sciences, Tohoku University, Aoba 6-6-05, Aramaki, Sendai 980-8579, Japan
ISSN:
0178-4617
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18140116
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Accession Number:
edscal.18140116
Database:
PASCAL Archive

Further Information

Several results on the monotone circuit complexity and the conjunctive complexity, i.e., the minimal number of AND gates in monotone circuits, of quadratic Boolean functions are proved. We focus on the comparison between single level circuits, which have only one level of AND gates, and arbitrary monotone circuits, and show that there is an exponential gap between the conjunctive complexity of single level circuits and that of general monotone circuits for some explicit quadratic function. Nearly tight upper bounds on the largest gap between the single level conjunctive complexity and the general conjunctive complexity over all quadratic functions are also proved. Moreover, we describe the way of lower bounding the single level circuit complexity and give a set of quadratic functions whose monotone complexity is strictly smaller than its single level complexity.