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An Introduction to Desriptional Complexity of Regular Languages through Analytic Combinatorics

Nowadays, an increasing attention is being given to the study of the descriptional complexity on the average case. Although the underlying theory for such a study seems intimidating, one can obtain interesting results in this area without too much effort. In this gentle introduction we take the reader on a journey through the basic analytical tools of that theory, giving some illustrative examples using regular expressions. We finalize with some new asymptotic average case results for several e-NFA constructions, presented in a unified framework.