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New Results on Alternating and Non-Deterministic Two-Dimensional Finite-State Automata


  • Jarkko Kari
  • Cristopher Moore


We resolve several long-standing open questions regarding the power of various types of finite-state automata to recognize "picture languages," i.e. sets of two-dimensional arrays of symbols. We show that the languages recognized by 4-way alternating finite-state automata (AFAs) are incomparable to the so-called tiling recognizable languages. Specifically, we show that the set of acyclic directed graphs is AFA-recognizable but not tiling recognizable, while the set of non-acyclic directed graphs is tiling recognizable but not AFA-recognizable. More generally, the complement of an AFA-recognizable language is tiling recognizable, and therefore the AFA-recognizable languages are not closed under complement. We also show that the set of languages recognized by 4-way NFAs is not closed under complement, and that NFAs are more powerful than DFAs, even for languages over one symbol.

Suggested Citation

  • Jarkko Kari & Cristopher Moore, 2000. "New Results on Alternating and Non-Deterministic Two-Dimensional Finite-State Automata," Working Papers 00-09-051, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:00-09-051

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