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Decision Problems for Restricted Variants of Two-Dimensional Automata

  • Taylor J. SmithEmail author
  • Kai SalomaaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11601)

Abstract

A two-dimensional finite automaton has a read-only input head that moves in four directions on a finite array of cells labelled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves, while a two-way two-dimensional automaton can only move downward and rightward.

We show that the language emptiness problem for unary three-way nondeterministic two-dimensional automata is Open image in new window -complete, and is in Open image in new window for general-alphabet two-way nondeterministic two-dimensional automata. We show that the language equivalence problem for two-way deterministic two-dimensional automata is decidable. This is the first known positive decidability result for the equivalence problem on two-dimensional automata over a general alphabet. We show that there exists a unary three-way deterministic two-dimensional automaton with a nonregular column projection, and we show that the row projection of a unary three-way nondeterministic two-dimensional automaton is always regular.

Keywords

Decision problem Language emptiness Language equivalence Three-way automata Two-dimensional automata Two-way automata 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of ComputingQueen’s UniversityKingstonCanada

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