Three-way automata on rectangular tapes over a one-letter alphabet
Information Sciences: an International Journal
Two-dimensional finite state recognizability
Fundamenta Informaticae - Special issue on formal language theory
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Recognizability of rectangular pictures by Wang systems
Journal of Automata, Languages and Combinatorics
A characterization of recognizable picture languages by tilings by finite sets
Theoretical Computer Science - Special issue on Caen '97
Introduction To Automata Theory, Languages, And Computation
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Star-Free Picture Expressions are Strictly Weaker Than First-Order Logic
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STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
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IBM Journal of Research and Development
Automata on a 2-dimensional tape
FOCS '67 Proceedings of the 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)
New operations and regular expressions for two-dimensional languages over one-letter alphabet
Theoretical Computer Science - The art of theory
Fundamenta Informaticae - Machines, Computations and Universality, Part II
On the complexity of unary tiling-recognizable picture languages
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Simulating two-dimensional recognizability by pushdown and queue automata
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
Fundamenta Informaticae - Machines, Computations and Universality, Part II
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The aim of this paper is to give regular expressions for two-dimensional picture languages. The paper focuses on a one-letter alphabet case, that corresponds to the study of “shapes” of families of pictures. A new diagonal concatenation operation is defined. Languages denoted by regular expressions with union, diagonal concatenation and its closure are characterized both in terms of rational relations and in terms of two-dimensional automata moving only right and down. The class of languages denoted by regular expressions with union, column, row and diagonal concatenation, and their closures are included in REC and strictly contains languages defined by three-way automata, but they are not comparable with ones defined by four-way automata. In order to encompass a wider class of languages, we propose some new operations that define languages that still lie in REC.