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.
The main part of this work was done at the University of Hamburg
Supported in part by ESPRIT Basic Research Action WG 6317: Algebraic and Syntactic Methods in Computer Science (ASMICS 2)
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© 1995 Springer-Verlag Berlin Heidelberg
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Petersen, H. (1995). Some results concerning two-dimensional turing machines and finite automata. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_69
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DOI: https://doi.org/10.1007/3-540-60249-6_69
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