On computing the entropy of cellular automata

Theoretical Computer Science

Volumn 290, Issue 3, 2003, Pages 1629-1646

  D'amico, Michele ^a   Manzini, Giovanni ^b   Margara, Luciano ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF EASTERN PIEDMONT   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CELLULAR AUTOMATA; ENTROPY; TOPOLOGY;

ERGODIC THEORY; TOPOLOGICAL ENTROPY;

DYNAMICAL SYSTEMS;

EID: 84994021855     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(02)00071-3     Document Type: Article

References (18)

1. [1] Amoroso, S., Patt, Y.N., Decision procedures for surjectivity and injectivity of parallel maps for tesselation structures. J. Comput. System Sci. 6 (1972), 448–464.
2. [2] Blanchard, F., Kurka, P., Maass, A., Topological and measure-theoretic properties of one-dimensional cellular automata. Physica D 103 (1997), 86–99.
3. m. Theoret. Comput. Sci. 233:1–2 (2000), 147–164.
4. [4] Hedlund, G.A., Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3 (1969), 320–375.
5. [5] Hurd, L.P., Kari, J., Culik, K., The topological entropy of cellular automata is uncomputable. Ergodic Theory Dynamical Systems 12 (1992), 255–265.
6. m. J. Comput. System Sci. 27 (1983), 125–140.
7. [7] Kari, J., The nilpotency problem of one-dimensional cellular automata. SIAM J. Comput. 21:3 (1992), 571–586.
8. [8] Kari, J., Reversibility and surjectivity problems of cellular automata. J. Comput. System Sci. 48:1 (1994), 149–182.
9. [9] Kurka, P., Languages, equicontinuity and attractors in cellular automata. Ergodic Theory Dynamical Systems 17 (1997), 417–433.
10. m: Algorithmic and dynamical aspects. J. Comput. System Sci. 56:1 (1998), 60–67.
11. [11] Manzini, G., Margara, L., Attractors of D-dimensional linear cellular automata. J. Comput. System Sci. 58:3 (1999), 597–610.
12. m. Theoret. Comput. Sci. 221 (1999), 157–177.
13. [13] G. Morris, Dynamical constraints on group actions, Ph.D. Thesis, University of East Anglia, 1998.
14. [14] Morris, G., Ward, T., Entropy bounds for endomorphisms commuting with K actions. Israel J. Math. 106 (1998), 1–12.
15. [15] M. Nasu, Maps in symbolic dynamics, Lecture Notes of the 10th KAIST Mathematics Workshop, 1995.
16. [16] Nasu, M., Textile systems for endomorphisms and automorphisms of the shift. Mem. Amer. Math. Soc., 114(546), 1995.
17. [17] Shereshevsky, M.A., Lyapunov exponents for one-dimensional cellular automata. J. Nonlinear Sci., 2(1), 1992, 1.
18. [18] Shereshevsky, M.A., Expansiveness, entropy and polynomial growth for groups acting on subshifts by automorphisms. Indag. Math. 4 (1993), 203–210.