Context-Free Languages of Sub-exponential Growth

Context-Free Languages of Sub-exponential Growth

There do not exist context–free languages of intermediate growth. The function γ whose value at each non–negative integer n is the number of words on length n in a fixed formal language L is called the growth function of L. Flajolet [3] asked if there are context–free languages of intermediate growth; that is, such that γ is not bounded above by a polynomial, but lim sup γ(n)/r = 0 for all r > ...

Growth-sensitivity of context-free languages

A language L over a )nite alphabet is called growth-sensitive if forbidding any set of subwords F yields a sub-language L whose exponential growth rate is smaller than that of L. It is shown that every (essentially) ergodic non-linear context-free language of convergent type is growth-sensitive. “Ergodic” means that the dependency di-graph of the generating context-free grammar is strongly conn...

Growth and Ergodicity of Context-free Languages

A language L over a finite alphabet Σ is called growth-sensitive if forbidding any set of subwords F yields a sublanguage LF whose exponential growth rate is smaller than that of L. It is shown that every ergodic unambiguous, nonlinear context-free language is growth-sensitive. “Ergodic” means for a context-free grammar and language that its dependency di-graph is strongly connected. The same r...

Context - Free Languages and

Context-Free Languages, Coalgebraically

We give a coalgebraic account of context-free languages using the functor D(X) = 2 × X for deterministic automata over an alphabet A, in three different but equivalent ways: (i) by viewing context-free grammars as D-coalgebras; (ii) by defining a format for behavioural differential equations (w.r.t. D) for which the unique solutions are precisely the context-free languages; and (iii) as theD-co...