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Some results concerning two-dimensional turing machines and finite automata

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

Abstract

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.

Keywords

Turing Machine Finite Automaton Input Tape Logarithmic Space Deterministic Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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