Semirings, automata, languages
Semirings, automata, languages
Rational series and their languages
Rational series and their languages
Recognizable picture languages
Parallel image processing
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
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
On Logics, Tilings, and Automata
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
On Piecewise Testable, Starfree, and Recognizable Picture Languages
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
Automata on a 2-dimensional tape
FOCS '67 Proceedings of the 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)
Weighted automata and weighted logics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Characterizations of recognizable picture series
Theoretical Computer Science
Weighted automata and weighted logics
Theoretical Computer Science
Weighted Distributed Systems and Their Logics
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Weighted Logics for Nested Words and Algebraic Formal Power Series
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Deterministic and unambiguous two-dimensional languages over one-letter alphabet
Theoretical Computer Science
Weighted automata and weighted logics with discounting
Theoretical Computer Science
A computational model for tiling recognizable two-dimensional languages
Theoretical Computer Science
Definable transductions and weighted logics for texts
Theoretical Computer Science
Definable transductions and weighted logics for texts
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Weighted automata and weighted logics with discounting
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
Weighted muller tree automata and weighted logics
Journal of Automata, Languages and Combinatorics
MSO logics for weighted timed automata
Formal Methods in System Design
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Multi-Valued MSO Logics OverWords and Trees
Fundamenta Informaticae
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The theory of two-dimensional languages, generalizing formal string languages, was motivated by problems arising from image processing and models of parallel computing. Weighted automata and series over pictures map pictures to some semiring and provide an extension to a quantitative setting. We establish a notion of a weighted MSO logics over pictures. The semantics of a weighted formula will be a picture series. We introduce weighted 2-dimensional online tessellation automata (W2OTA) extending the common automata-theoretic model for picture languages. We prove that the class of picture series defined by sentences of the weighted logics coincides with the family of picture series that are computable by W2OTA. Moreover, behaviours of W2OTA coincide precisely with the recognizable picture series characterized in [18].