An example of an indexed language of intermediate growth

AbstractWe give an example of a language belonging to the class of indexed languages whose growth is intermediate. In particular, the growth function of this language is transcendental

On the growth of linear languages

AbstractIt is well known that the growth of a context-free language is either polynomial or exponential. However no algorithm for such an alternative is known. In this article we determine such an algorithm for the subclass of unambiguous linear languages

From indexed grammars to generating functions

We extend the Chomsky/Sch\"utzenberger method of computing the growth series of an unambiguous context-free language to the larger class of indexed languages. We illustrate the technique with numerous examples.Comment: 23 pages, 3 figure

Groups, Graphs, Languages, Automata, Games and Second-order Monadic Logic

In this paper we survey some surprising connections between group theory, the theory of automata and formal languages, the theory of ends, infinite games of perfect information, and monadic second-order logic