Growth and ergodicity of context-free languages

Author:

Ceccherini-Silberstein Tullio,Woess Wolfgang

Abstract

A language L L over a finite alphabet Σ \boldsymbol \Sigma is called growth-sensitive if forbidding any set of subwords F F yields a sublanguage L F L^{F} whose exponential growth rate is smaller than that of L 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 result as above holds for the larger class of essentially ergodic context-free languages, and if growth is considered with respect to the ambiguity degrees, then the assumption of unambiguity may be dropped. The methods combine a construction of grammars for 2 2 -block languages with a generating function technique regarding systems of algebraic equations.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference40 articles.

1. [1] G. N. Arzhantseva and I. G. Lysenok, Growth tightness for word hyperbolic groups, preprint, Univ. Genève, \url{http://www.unige.ch/math/biblio/preprint/pp2001.html}, 2001.

2. [2] L. Bartholdi and T. G. Ceccherini-Silberstein, Growth series and random walks on some hyperbolic graphs, in print, Monatsh. Math (2002).

3. [3] M. R. Bridson and R. H. Gilman, Context-free languages of sub-exponential growth, preprint, \url{http://attila.stevens-tech.edu/ rgilman/}, 1999.

4. [4] T. Ceccherini-Silberstein, F. Fiorenzi and F. Scarabotti, The Garden of Eden theorem for cellular automata and for symbolic dynamical systems, to appear, Proceedings of the workshop “Random walks and geometry” held at Erwin Schroedinger Institute for Mathematical Physics, Vienna, Austria, 18.06-13.07 2001. Vadim A. Kaimanovich, Klaus Schmidt, Wolfgang Woess, editors. De Gruyter, Berlin, 2002.

5. [5] T. Ceccherini-Silberstein and F. Scarabotti, Random walks, entropy and hopfianity of free groups, to appear, Proceedings of the workshop “Random walks and geometry” held at Erwin Schroedinger Institute for Mathematical Physics, Vienna, Austria, 18.06-13.07 2002. Vadim A. Kaimanovich, Klaus Schmidt, Wolfgang Woess, editors. De Gruyter, Berlin, 2002.

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