论文信息 - The topological entropy of cellular automata is uncomputable

The topological entropy of cellular automata is uncomputable

Abstract There is no algorithm which will take a description of a celluar automaton and determine whether it has zero topological entropy, or for any fixed ε > 0 compute its topological entropy to a tolerance e. Furthermore a set of aperiodic Wang tiles arising from Penrose's kite and dart tiles is used to demonstrate specific examples of cellular automata with a single periodic point but non-trivial non-wandering sets, which furthermore can be constructed to have arbitrarily high topological entropy.

K. Culík | L. Hurd | J. Kari

[1] Hao Wang,et al. Proving theorems by pattern recognition I , 1960, Commun. ACM.

[2] Hao Wang. Proving theorems by pattern recognition — II , 1961 .

[3] Robert L. Berger. The undecidability of the domino problem , 1966 .

[4] Marvin Minsky,et al. Computation : finite and infinite machines , 2016 .

[5] F. P. Kaminger. The Noncomputability of the Channel Capacity of Context-Senstitive Languages , 1970, Inf. Control..

[6] R. Robinson. Undecidability and nonperiodicity for tilings of the plane , 1971 .

[7] P. Walters. Introduction to Ergodic Theory , 1977 .

[8] E. Coven. Topological entropy of block maps , 1980 .

[9] Lyman P. Hurd. Formal Language Characterization of Cellular Automaton Limit Sets , 1987, Complex Syst..

[10] Karel Culik,et al. On Invertible Cellular Automata , 1987, Complex Syst..

[11] D. Lind. Entropies of automorphisms of a topological Markov shift , 1987 .

[12] Lyman P. Hurd. The Non-wandering Set of a CA Map , 1988, Complex Syst..

[13] G. C. Shephard,et al. Tilings and Patterns , 1990 .

[14] Jarkko Kari. The Nilpotency Problem of One-Dimensional Cellular Automata , 1992, SIAM J. Comput..