A combinatorial analogue of the Jacobian problem in automata networks

Advances in Applied Mathematics

Volumn 34, Issue 1, 2005, Pages 30-46

  Shih, Mau Hsiang ^a   Dong, Jian Lang ^a  

^a NATIONAL TAIWAN NORMAL UNIVERSITY   (Taiwan)

Author keywords

01 strings; Automata network; Boolean eigenvalue; Discrete Jacobian matrix; Fixed point; Hamming metric; Hypercube; Jacobian conjecture; k subcube

Indexed keywords

BOOLEAN ALGEBRA; COMBINATORIAL MATHEMATICS; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA;

AUTOMATA NETWORK; BOOLEAN EIGENVALUE; DISCRETE JACOBIAN MATRIX; HAMMING METRIC; HYPERCUBE; JACOBIAN CONJECTURE;

AUTOMATA THEORY;

EID: 10244247793     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aam.2004.06.002     Document Type: Article

References (7)

1. F. Robert, Théorèmes de Perron Frobenius et Stein Rosenberg booléens, Linear Algebra Appl. 19 (1978) 237-250.
2. F. Robert, Itérations sur des ensembles finis et automates cellulaires contractants, Linear Algebra Appl. 29 (1980) 393-412.
3. F. Robert, Dérivée discrète et convergence local d'une itération booléenne, Linear Algebra Appl. 52 (1983) 547-589.
4. F. Robert, Discrete Iterations, A Metric Study, Springer Ser. Comput. Math., vol. 6, Springer-Verlag, Berlin- Heidelberg-New York, 1986.
5. F. Robert, Les Systémes Dynamiques Discrets, Mathématiques & Applications, vol. 19, Springer-Verlag, Berlin-Heidelberg-New York, 1995.
6. M.-H. Shih, J.-L. Ho, Solution of the boolean Markus-Yamabe problem, Adv. in Appl. Math. 22 (1999) 60-102.
7. M.-H. Shih, Y.-Y. Lur, Products of matrices ofzeros and ones, preprint.