Descriptive complexity for pictures languages

Etienne Grandjean (1) , Frédéric Olive (2)

1 Equipe AMACC - Laboratoire GREYC - UMR6072
2 LIF - Laboratoire d'informatique Fondamentale de Marseille

This paper deals with logical characterizations of picture languages of any dimension by syntactical fragments of existential second-order logic. Two classical classes of picture languages are studied: - the class of recognizable picture languages, i.e. projections of languages defined by local constraints (or tilings): it is known as the most robust class extending the class of regular languages to any dimension; - the class of picture languages recognized on nondeterministic cellular automata in linear time : cellular automata are the simplest and most natural model of parallel computation and linear time is the minimal time-bounded class allowing synchronization of nondeterministic cellular automata.

Mots clés: descriptive complexity; picture languages; recognizability; cellular automata; computational complexity; nondeterminism; second-order logic; linear time

Domaines: Complexité [cs.CC]

Etienne Grandjean, Frédéric Olive. Descriptive complexity for pictures languages. Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL, CSL 2012, September 3-6, 2012, Fontainebleau, France, Sep 2012, Fontainebleau, France. pp.1-15. ⟨hal-00779971⟩