6 research outputs found
Descriptive complexity for pictures languages
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.
We uniformly generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of "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. 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
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
Definability by Horn Formulas and Linear Time on Cellular Automata
We establish an exact logical characterization of linear time complexity of cellular automata of dimension d, for any fixed d: a set of pictures of dimension d belongs to this complexity class iff it is definable in existential second-order logic restricted to monotonic Horn formulas with built-in successor function and d+1 first-order variables. This logical characterization is optimal modulo an open problem in parallel complexity. Furthermore, its proof provides a systematic method for transforming an inductive formula defining some problem into a cellular automaton that computes it in linear time
Definability by Horn formulas and linear time on cellular automata
International audienceWe establish an exact logical characterization of linear time complexity of cellular automata of dimension d, for any fixed d: a set of pictures of dimension d belongs to this complexity class iff it is definable in existential second-order logic restricted to monotonic Horn formulas with built-in successor function and d + 1 first-order variables. This logical characterization is optimal modulo an open problem in parallel complexity. Furthermore, its proof provides a systematic method for transforming an inductive formula defining some problem into a cellular automaton that computes it in linear time
Descriptive complexity for pictures languages
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. We uniformly generalize to any dimension the characterization by Giammarresi et al. [7] of the class of 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. 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 âregularâ structures