  An elementary application of Algorithmic Complexity Theory to the polygonal
approximations of curved billiards-integrable and chaotic-unveils the
equivalence of this problem to the procedure of quantization of classical
systems: the scaling relations for the average complexity of symbolic
trajectories are formally the same as those governing the semi-classical limit
of quantum systems. Two cases-the circle, and the stadium-are examined in
detail, and are presented as paradigms.
