Complex Systems

Partitions, Rational Partitions, and Characterization of Complexity Download PDF

Mario Casartelli
Dipartimento di Fisica dell'Universita di Parma,
Sezione Teorica, CNR, INFM, Italy


The quantitative characterization of complexity for several dynamic processes is approached by a mathematical scheme based on the metric and combinatorial properties of the space of finite measurable partitions. Precisely, is embedded in a larger space of new objects, "rational partitions,'' describing the antisimilarity between two probabilistic experiments. Rational partitions consist of properly reduced couples of ordinary partitions, and their main features are briefly reviewed. An extended entropy functional in allows the introduction of indicators sensitive to different possible aspects of complexity for cellular automata, shifts, mappings, etc. These indicators appear to be accessible to numerical experiments in many nontrivial situations.