Picture Languages: From Wang Tiles to 2D Grammars

Cherubini, Alessandra; Pradella, Matteo

doi:10.1007/978-3-642-03564-7_2

Cited by 11 publications

(4 citation statements)

References 53 publications

(52 reference statements)

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“…These results consolidate and strengthen the notions of determinism and unambiguity of two-dimensional languages here introduced. Finally, a very recent survey on two-dimensional languages can be found in [13].…”

Section: Introductionmentioning

confidence: 99%

Deterministic and Unambiguous Families within Recognizable Two-dimensional Languages

Anselmo

Giammarresi

Madonia

2010

Fundamenta Informaticae

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Recognizable two-dimensional languages (REC) are defined by tiling systems that generalize to two dimensions non-deterministic finite automata for strings. We introduce the notion of deterministic tiling system and the corresponding family of languages (DREC) and study its structural and closure properties. Furthermore we show that, in contrast with the one-dimensional case, there exist other classes between deterministic and non-deterministic families that we separate by means of examples and decidability properties.

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Section: Introductionmentioning

confidence: 99%

Deterministic and Unambiguous Families within Recognizable Two-dimensional Languages

Anselmo

Giammarresi

Madonia

2010

Fundamenta Informaticae

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“…The well-known solution to avoid using labels in sequential programming is to use "structured programming" based on a particular class of regular expressions. 6 Renaming is also used in getting regular expressions for Petri nets [13] and timed automata [1]. Remark: Corner composition should be used with care.…”

Section: 2(b)mentioning

confidence: 99%

“…Comments: A basic operation here is the substitution of 2-dimensional word languages for the variables X i used in these equations. A similar operation, but restricted to rectangular words, has been used in [5,6] to define tile grammars. Our formalism, using arbitrary shape words, may be seen as a generalization of this mechanism.…”

Section: Systems Of Recursive Equationsmentioning

confidence: 99%

Self-Assembling Interactive Modules: A Research Programme

Ştefănescu¹

2016

From Action Systems to Distributed Systems

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In this paper we propose a research programme for getting structural characterisations for 2-dimensional languages generated by self-assembling tiles. This is part of a larger programme on getting a formal foundation of parallel, interactive, distributed systems. Tiling -a brief introductionTiling is an old and popular subject [15]. While our focus is on 2dimensional tiles/tiling and 2-dimensional regular expressions, the formalism itself can be easily extended to cope with 3, 4, or more dimensions.An interesting tiling problem was proposed by Wang in 1961. Wang tiles are: (1) finite sets of unit squares, with a color on each side; (2) which can not be rotated or reflected; and (3) such that there is an infinite number of copies from each tile. A tiling is a side-by-side arrangement of tiles, such that neighbouring tiles have the same color on the common borders. The

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“…The literature on picture languages is quite rich of models, see e.g. [14,12,17,9,5,7,3,8]. Here we regard class REC, introduced in [12] with the aim to generalize to 2D the class of regular string languages.…”

Section: Introductionmentioning

confidence: 99%

Picture Recognizability with Automata Based on Wang Tiles

Lonati

Pradella

2010

SOFSEM 2010: Theory and Practice of Computer Science

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Abstract. We introduce a model of automaton for picture language recognition which is based on tiles and is called Wang automaton, since its description relies on the notation of Wang systems. Wang automata combine features of both online tessellation acceptors and 4-ways automata: as in online tessellation acceptors, computation assigns states to each picture position; as in 4-way automata, the input head visits the picture moving from one pixel to an adjacent one, according to some scanning strategy. We prove that Wang automata recognize the class REC, i.e. they are equivalent to tiling systems or online tessellation acceptors, and hence strictly more powerful than 4-way automata. We also consider a very natural notion of determinism for Wang automata, and study the resulting class, comparing it with other deterministic classes considered in the literature, like DREC and Snake-DREC.

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Picture Languages: From Wang Tiles to 2D Grammars

Cited by 11 publications

References 53 publications

Deterministic and Unambiguous Families within Recognizable Two-dimensional Languages

Deterministic and Unambiguous Families within Recognizable Two-dimensional Languages

Self-Assembling Interactive Modules: A Research Programme

Picture Recognizability with Automata Based on Wang Tiles

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