Fixed points and maximal independent sets in AND-OR networks

Aracena, J; Demongeot, J.; Goles, E.

Abstract

We study the maximum number of fixed points of boolean networks with local update function AND-OR. We prove that this number for networks with connected digraph is 2(n-1)/2 for n odd and 2(n-2)/2+1 for n even if the digraph has not loops; and 2n-1+1 otherwise, where n is the number of nodes of the digraph. We also exhibit some networks reaching these bounds. To obtain these results we construct a bijection between the maximal independent sets of the digraph and the fixed points of the network belonging to a particular family of AND-OR networks. © 2003 Elsevier B.V. All rights reserved.

Más información

Título según WOS: Fixed points and maximal independent sets in AND-OR networks
Título según SCOPUS: Fixed points and maximal independent sets in AND-OR networks
Título de la Revista: DISCRETE APPLIED MATHEMATICS
Volumen: 138
Número: 3
Editorial: ELSEVIER SCIENCE BV
Fecha de publicación: 2004
Página de inicio: 277
Página final: 288
Idioma: English
DOI:

10.1016/S0166-218X(03)0046-1X

Notas: ISI, SCOPUS