Deterministic Complexity and Entropy

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.