We give a characterization, in terms of computational complexity, of the family Rec 1 of the unary picture languages that are tiling recognizable. We introduce quasi-unary strings to represent unary pictures and we prove that any unary picture language L is in Rec 1 if and only if the set of all quasi-unary strings encoding the elements of L is recognizable by a one-tape nondeterministic Turing machine that is space and head-reversal linearly bounded. In particular, the result implies that the family of binary string languages corresponding to tiling-recognizable square languages lies between NTime(2 n ) and NTime(4 n ). This also implies the existence of a nontiling-recognizable unary square language that corresponds to a binary string language recognizable in nondeterministic time O(4 n logn).

On the complexity of unary tiling-recognizable picture languages / A. Bertoni, M. Goldwurm, V. Lonati (LECTURE NOTES IN COMPUTER SCIENCE). - In: STACS 2007 / [a cura di] W. Thomas, P. Weil. - Prima edizione. - Berlin : Springer, 2007. - ISBN 9783540709176. - pp. 381-392 (( Intervento presentato al 24. convegno Annual Symposium on Theoretical Aspects of Computer Science tenutosi a Aachen nel 2007 [10.1007/978-3-540-70918-3_33].

On the complexity of unary tiling-recognizable picture languages

A. Bertoni
Primo
;
M. Goldwurm
Secondo
;
V. Lonati
Ultimo
2007

Abstract

We give a characterization, in terms of computational complexity, of the family Rec 1 of the unary picture languages that are tiling recognizable. We introduce quasi-unary strings to represent unary pictures and we prove that any unary picture language L is in Rec 1 if and only if the set of all quasi-unary strings encoding the elements of L is recognizable by a one-tape nondeterministic Turing machine that is space and head-reversal linearly bounded. In particular, the result implies that the family of binary string languages corresponding to tiling-recognizable square languages lies between NTime(2 n ) and NTime(4 n ). This also implies the existence of a nontiling-recognizable unary square language that corresponds to a binary string language recognizable in nondeterministic time O(4 n logn).
unary picture languages; tiling systems; Turing machine head reversal
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/28988
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