On the Complexity of Unary Tiling-Recognizable Picture Languages

Abstract. We give a characterization, in terms of computational complexity, of the family Rec1 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 Rec1 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(2n ) and NTime(4n ). This also implies the existence of a nontiling-recognizable unary square language that corresponds to a binary string language recognizable in nondeterministic time O(4n log n). Classification: automata and formal languages, computational complexity.

• Type: Conference
• Year: 2007
• Where: STACS
• Authors: Alberto Bertoni, Massimiliano Goldwurm, Violetta Lonati
• Keywords: Binary String Language, Computational Complexity, STACS 2007, Theoretical Computer Science, Unary Picture Language