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Descriptive complexity for pictures languages (extended abstract)
This paper deals with descriptive complexity of picture languages of any
dimension by syntactical fragments of existential second-order logic.
- We uniformly generalize to any dimension the characterization by
Giammarresi et al. \cite{GRST96} of the class of \emph{recognizable} picture
languages in existential monadic second-order logic. - We state several logical
characterizations of the class of picture languages recognized in linear time
on nondeterministic cellular automata of any dimension. They are the first
machine-independent characterizations of complexity classes of cellular
automata.
Our characterizations are essentially deduced from normalization results we
prove for first-order and existential second-order logics over pictures. They
are obtained in a general and uniform framework that allows to extend them to
other "regular" structures. Finally, we describe some hierarchy results that
show the optimality of our logical characterizations and delineate their
limits.Comment: 33 pages - Submited to Lics 201