On the Complexity of Unary Tiling-Recognizable Picture Languages

  • Alberto Bertoni
  • Massimiliano Goldwurm
  • Violetta Lonati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)


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).

Classification: automata and formal languages, computational complexity.


unary picture languages tiling systems Turing machine head reversal. 


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Alberto Bertoni
    • 1
  • Massimiliano Goldwurm
    • 1
  • Violetta Lonati
    • 1
  1. 1.Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, Via Comelico 39/41, 20135 Milano –Italy

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