Chapter

Automata, Languages and Programming

Volume 1443 of the series Lecture Notes in Computer Science pp 470-481

Date:

On computing the entropy of cellular automata

  • Michele D'amicoAffiliated withDipartimento di Matematica, Università di Bologna
  • , Giovanni ManziniAffiliated withDipartimento di Scienze e Tecnologie Avanzate, Università di TorinoIstituto di Matematica Computazionale
  • , Luciano MargaraAffiliated withDipartimento di Scienze dell'Informazione, Università di Bologna

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Abstract

We show how to compute the entropy of two important classes of cellular automata namely, linear and positively expansive cellular automata. In particular, we prove a closed formula for the topological entropy of D-dimensional (D ≥ 1) linear cellular automata over the ring Z m (m ≥ 2) and we provide an algorithm for computing the topological entropy of positively expansive cellular automata.