A survey of two-dimensional automata theory
Information Sciences: an International Journal
Monadic second-order logic over rectangular pictures and recognizability by tiling systems
Information and Computation
Two-dimensional finite state recognizability
Fundamenta Informaticae - Special issue on formal language theory
Recognizable picture languages and domino tiling
Theoretical Computer Science
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
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
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
Tile rewriting grammars and picture languages
Theoretical Computer Science - The art of theory
Collage of two-dimensional words
Theoretical Computer Science - The art of theory
Two-dimensional formal languages and pattern recognition by cellular automata
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Automata on a 2-dimensional tape
FOCS '67 Proceedings of the 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)
Weighted picture automata and weighted logics
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Note: Schützenberger's theorem on formal power series follows from Kleene's theorem
Theoretical Computer Science
Valuations of weighted automata: doing it in a rational way
Algebraic Foundations in Computer Science
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The theory of two-dimensional languages as a generalization of formal string languages was motivated by problems arising from image processing and pattern recognition, and also concerns models of parallel computing. Here we investigate power series on pictures. These are functions that map pictures to elements of a semiring and provide an extension of two-dimensional languages to a quantitative setting. We assign weights to different devices, ranging from picture automata to tiling systems. We will prove that, for commutative semirings, the behaviours of weighted picture automata are precisely alphabetic projections of series defined in terms of rational operations, and also coincide with the families of series characterized by weighted tiling or weighted domino systems.