Tile rewriting grammars and picture languages
TLDR
It is proved this model has greater generative capacity than the tiling systems of Giammarresi and Restivo and the grammars of Matz, another generalization of context-free string Grammars to 2D.About:
This article is published in Theoretical Computer Science.The article was published on 2005-06-27 and is currently open access. It has received 41 citations till now. The article focuses on the topics: Tree-adjoining grammar & Context-sensitive grammar.read more
Citations
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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.
Journal Article
Weighted picture automata and weighted logics
TL;DR: This work introduces weighted 2-dimensional online tessellation automata (W2OTA) extending the common automata-theoretic model for picture languages and proves that the class of picture series defined by sentences of the weighted logics coincides with the family ofPicture series that are computable by W2OTA.
Book ChapterDOI
Weighted picture automata and weighted logics
TL;DR: 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.
Journal ArticleDOI
Weighted Picture Automata and Weighted Logics
TL;DR: In this article, a notion of a weighted MSO logics over pictures is introduced and the semantics of a weighted MSO will be a picture series, and it is shown that for commutative semirings, the class of picture series defined by sentences of the weighted logics coincides with the family of picture-series that are computable by W2OTA.
Journal ArticleDOI
A unifying approach to picture grammars
TL;DR: In this paper, the authors focus on a simple type of tiling, named regional, and define the corresponding regional tile grammars, which can be unified and extended using an approach, whereby the right part of a rule is formalized by means of a finite set of permitted tiles.
References
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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.
Journal ArticleDOI
Recognizable picture languages
Dora Giammarresi,Antonio Restivo +1 more
TL;DR: A new notion of recognizability for picture (two-dimensional) languages is proposed extending the characterization of one-dimensional recognizable languages in terms of local languages and alphabetic mappings and the undecidability of the emptiness problem is proved.
Journal ArticleDOI
Some properties of two-dimensional on-line tessellation acceptors
Katsushi Inoue,Akira Nakamura +1 more
TL;DR: The purpose of this paper is to propose a new type acceptor called the “two-dimensional on-line tessellation acceptor” (denoted by “2-ota”) and to examine several properties of the 2-ota, which might be considered as a real-time mode of rectangular array bounded cellular space.
Book ChapterDOI
Regular Expressions and Context-Free Grammars for Picture Languages
TL;DR: A new concept of regular expression and context-free grammar for picture languages (sets of matrices over a finite alphabet) is introduced and these two formalisms are compared and connected.
Book ChapterDOI
Bounded Parallelism in Array Grammars Used for Character Recognition
Henning Fernau,Rudolf Freund +1 more
TL;DR: The aim of this paper is to elaborate the power of cooperation in generating and analysing (handwritten) characters by array grammars by presenting various non-context-free sets of arrays generated by cooperating distributed array grammar systems with prescribed teams working in different modes.