The Complexity of Unary Tiling Recognizable Picture Languages: Nondeterministic and Unambiguous Cases

  • Authors:

  • Alberto Bertoni;Massimiliano Goldwurm;Violetta Lonati

  • Affiliations:

  • Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano Via Comelico 39/41, 20135 Milano - Italy. {bertoni, goldwurm, lonati}@dsi.unimi.it;(Correspd.) Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano Via Comelico 39/41, 20135 Milano - Italy. {bertoni, goldwurm, lonati}@dsi.unimi.it;Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano Via Comelico 39/41, 20135 Milano - Italy. {bertoni, goldwurm, lonati}@dsi.unimi.it

  • Venue:
  • Fundamenta Informaticae - Machines, Computations and Universality, Part II
  • Year:
  • 2009

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Abstract

In this paper we consider the classes REC1 and UREC1 of unary picture languages that are tiling recognizable and unambiguously tiling recognizable, respectively. By representing unary pictures by quasi-unary strings we characterize REC1 (resp. UREC1) as the class of quasi-unary languages recognized by nondeterministic (resp. unambiguous) linearly space-bounded one-tape Turing machines with constraint on the number of head reversals. We apply such a characterization in two directions. First we prove that the binary string languages encoding tiling recognizable unary square languages lies between NTIME(2n) and NTIME(4n); by separation results, this implies there exists a non-tiling recognizable unary square language whose binary representation is a language in NTIME(4n log n). In the other direction, by means of results on picture languages, we are able to compare the power of deterministic, unambiguous and nondeterministic one-tape Turing machines that are linearly space-bounded and have constraint on the number of head reversals.