Concatenation Operations and Restricted Variants of Two-Dimensional Automata

Smith, Taylor J.; Salomaa, Kai

doi:10.48550/arxiv.2008.11164

2020

DOI: 10.48550/arxiv.2008.11164

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Concatenation Operations and Restricted Variants of Two-Dimensional Automata

Taylor J. Smith

Kai Salomaa

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Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata

Smith

Salomaa

2020

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The row projection (resp., column projection) of a two-dimensional language L is the one-dimensional language consisting of all first rows (resp., first columns) of each two-dimensional word in L. The operation of row projection has previously been studied under the name "frontier language", and previous work has focused on oneand two-dimensional language classes.In this paper, we study projections of languages recognized by various two-dimensional automaton classes. We show that both the row and column projections of languages recognized by (four-way) two-dimensional automata are exactly context-sensitive. We also show that the column projections of languages recognized by unary three-way two-dimensional automata can be recognized using nondeterministic logspace. Finally, we study the state complexity of projection languages for two-way two-dimensional automata, focusing on the language operations of union and diagonal concatenation.

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Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata

Smith

Salomaa

2020

Preprint

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Concatenation Operations and Restricted Variants of Two-Dimensional Automata

Cited by 1 publication

References 8 publications

Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata

Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata

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