Deterministic Complexity and Entropy

Authors:
Mark R. Titchener;Radu Nicolescu;Ludwig Staiger;Aaron Gulliver;Ulrich Speidel
Affiliations:
(Correspd.) Dept. of Computer Science, The University of Auckland, New Zealand. mark@tcode.auckland.ac.nz;Dept. of Computer Science, The University of Auckland, New Zealand;Institut für Informatik, Martin-Luther-Universitä Halle-Wittenberg, Germany;Dept. of Electrical & Computer Engineering, University of Victoria, Canada;Dept. of Computer Science, The University of Auckland, New Zealand
Venue:
Fundamenta Informaticae - Contagious Creativity - In Honor of the 80th Birthday of Professor Solomon Marcus
Year:
2005

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Abstract

Lempel and Ziv (1976) proposed a computable string production-complexity. In this paper, our emphasis is on providing the rigorous development, where possible, for the theoretical aspects of a more recent and contrasting measure of string complexity. We derive expressions for complexity bounds subject to certain constraints. We derive an analytic approximation to the upper bound to linearize the complexity measure. The linearized measure enables us to propose an entropy measure, observed elsewhere to correspond closely with the Kolmogorov-Sinai entropy in simple dynamical systems.