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
Handbook of formal languages, vol. 3
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
Introduction To Automata Theory, Languages, And Computation
Star-Free Picture Expressions are Strictly Weaker Than First-Order Logic
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Regular Expressions and Context-Free Grammars for Picture Languages
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
On Piecewise Testable, Starfree, and Recognizable Picture Languages
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
Regular expressions for two-dimensional languages over one-letter alphabet
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Deterministic and unambiguous two-dimensional languages over one-letter alphabet
Theoretical Computer Science
Picture Languages Generated by Assembling Tiles
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Picture Languages: From Wang Tiles to 2D Grammars
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
Tiling recognizable two-dimensional languages
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Recognizable vs. regular picture languages
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Deterministic two-dimensional languages over one-letter alphabet
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Simulating two-dimensional recognizability by pushdown and queue automata
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
Picture Languages Generated by Assembling Tiles
Fundamenta Informaticae - Theory that Counts: To Oscar Ibarra on His 70th Birthday
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We consider the problem of defining regular expressions to characterize the class of recognizable picture languages in the case of a one-letter alphabet. We define a diagonal concatenation and its star and consider two different families, L(D) and L(CRD), of languages denoted by regular expressions involving such operations plus classical operations. L(D) is characterized both in terms of rational relations and in terms of two-dimensional automata moving only right and down. L(CRD) is included in REC and contains languages defined by three-way automata while languages in L(CRD) necessarily satisfy some regularity conditions. Finally, we introduce new definitions of advanced stars expressing the necessity of conceptually different definitions for iteration.