Z(2)-algebras in the Boolean function irreducible decomposition
Por:
Takane, M, Zertuche, F
Publicada:
1 feb 2012
Resumen:
We develop further the consequences of the irreducible-Boolean classification established by Zertuche, ["On the robustness of NK-Kauffman networks against changes in their connections and Boolean functions," J. Math. Phys. 50, 043513 (2009)] which have the advantage of allowing strong statistical calculations in disordered Boolean function models, such as the NK-Kauffman networks. We construct a ring-isomorphism R-K {i(1), ..., i(lambda)} congruent to P-2[K] of the set of reducible K-Boolean functions that are reducible in the Boolean arguments with indexes {i(1), ... , i(lambda)}, and the double power set P-2[K] of the first K natural numbers. This allows us, among other things, to calculate the number Q(K)(lambda, omega) of K-Boolean functions which are lambda-irreducible with weight omega. Q(K)(lambda, omega) is a fundamental quantity in the study of the stability of NK-Kauffman networks against changes in their connections between their Boolean functions, as well as in the mean fie
Filiaciones:
Takane, M:
Univ Nacl Autonoma Mexico, Inst Matemat, Unidad Cuernavaca, Cuernavaca 62251, Mor, Mexico
Zertuche, F:
Univ Nacl Autonoma Mexico, Inst Matemat, Unidad Cuernavaca, Cuernavaca 62251, Mor, Mexico
|