Book ChapterDOI
Weighted picture automata and weighted logics
Ina Mäurer
- pp 313-324
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TLDR
In this article, the authors introduce weighted 2-dimensional online tessellation automata (W2OTA) extending the common automata-theoretic model for picture languages, and 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.Abstract:
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].read more
Citations
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Journal ArticleDOI
Weighted automata and weighted logics
Manfred Droste,Paul Gastin +1 more
TL;DR: A weighted version of MSO logic is introduced and it is proved that, for commutative semirings, the behaviours of weighted automata are precisely the formal power series definable with particular sentences of the authors' weighted logic.
Journal ArticleDOI
Unambiguous recognizable two-dimensional languages
TL;DR: It is proved that there are recognizable languages that are inherently ambiguous, that is UREC family is a proper subclass of REC family, and it is shown that it is undecidable whether a given tiling system is unambiguous.
Book ChapterDOI
Weighted automata and weighted logics on infinite words
Manfred Droste,George Rahonis +1 more
TL;DR: In this article, weighted automata over infinite words with Muller acceptance condition were introduced and their behaviors coincide with the semantics of weighted restricted MSO-sentences, and an equivalence property of weighted Muller and weighted Buchi automata was established over certain semirings.
Book ChapterDOI
Weighted logics for traces
TL;DR: The coincidence of recognizable trace series with those which are definable by restricted formulas from a weighted logics over traces is shown and the equivalence of aperiodic and first-order definable trace series is shown.
Journal ArticleDOI
Weighted automata and weighted logics with discounting
Manfred Droste,George Rahonis +1 more
TL;DR: A weighted logic with discounting is introduced and the Buchi-Elgot theorem is established for weighted automata over finite words and arbitrary commutative semirings and a purely syntactically defined weighted logic is obtained if the underlying semiring is additively locally finite.
References
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Book
Rational Series and Their Languages
TL;DR: This chapter discusses the development of Rational Series over a Principal Ring, a model based on the model developed in Chapter I, and its applications to Languages and Codes.
Book
Automata-theoretic aspects of formal power series
Arto Salomaa,Matti Soittola +1 more
TL;DR: The style has sometimes been characterized as austere or severe, but the author does expect the reader to be able to fill in the more obvious details and the author permits him to present the leading ideas in an uncluttered way.
Book
Syntactic Methods in Pattern Recognition
King-Sun Fu,Mark A. Aizerman +1 more
TL;DR: This book is an integrated sequence of papers Professor Michie has published, for a general audience, over the last decade or so.
Book ChapterDOI
Two-dimensional languages
Dora Giammarresi,Antonio Restivo +1 more
TL;DR: The aim of this chapter is to generalize concepts and techniques of formal language theory to two dimensions.