generating functions, grammars, algebra, combinatorics, syntax, complex analysis


A context-free grammar is a set of mathematical rules that classifies strings (sequences of symbols) as either "valid" or "invalid". Given a context-free grammar, the set of all "valid" strings is known as a context-free language. The counting sequence of a language is defined as the sequence of numbers stating how many strings of each length are elements of the language. Finally, the ordinary generating function of a sequence is the power series whose coefficients are the elements of the sequence. This paper investigates the properties of ordinary generating functions of counting sequences of context-free languages. We also discuss the Chomsky–Schützenberger Theorem, an important theorem about these generating functions.