Some results concerning two-dimensional turing machines and finite automata

  • H. Petersen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 965)


We show that emptiness is decidable for three-way two-dimensional nondeterministic finite automata as well as the universe problem for the corresponding class of deterministic automata. Emptiness is undecidable for three-way (and even two-way) two-dimensional alternating finite automata over a single-letter alphabet. Consequently inclusion, equivalence, and disjointness for these automata are undecidable properties.

We establish a hierarchy result for space bounded two-dimensional alternating Turing machines above logarithm where the languages witnessing the hierarchy are over single-letter alphabets. Below logarithm we prove that an infinite hierarchy of languages over larger alphabets exists.

The results rely mainly on a translational technique from one to two dimensions. Using this technique we can also show some connections between open problems of two-dimensional automata theory and one-dimensional complexity theory.


Turing Machine Finite Automaton Input Tape Logarithmic Space Deterministic Automaton 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • H. Petersen
    • 1
  1. 1.Institut für Informatik der Universität StuttgartStuttgart

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