Combinatorial Characterization of Formal Languages

This paper is an extended abstract of the dissertation presented by the author for the doctoral degree in physics and mathematics (in Russia). The main characteristic studied in the dissertation is combinatorial complexity, which is a "counting" function associated with a language and returning the number of words of given length in this language. For several classes of languages, a variety of problems about combinatorial complexity and its connections to other parameters of languages are studied. A brief introduction to the topic and the formulations of results are presented. No proofs are given; instead, the papers containing the proofs are cited.