Weighted Picture Automata and Weighted Logics

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Weighted Picture Automata and Weighted Logics
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].
Ina Fichtner
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where MST
Authors Ina Fichtner
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