# Two-Dimensional Languages

@inproceedings{Giammarresi1997TwoDimensionalL, title={Two-Dimensional Languages}, author={Dora Giammarresi and Antonio Restivo}, booktitle={Handbook of Formal Languages}, year={1997} }

The aim of this chapter is to generalize concepts and techniques of formal language theory to two dimensions. Informally, a two-dimensional string is called a picture and is defined as a rectangular array of symbols taken from a finite alphabet. A two-dimensional language (or picture language) is a set of pictures.

## 429 Citations

### Two-Dimensional Languages

- Computer Science
- 2004

A two-dimensional (2-d) language is a set of 2-d arrays of symbols, whose theories give the mathematical foundation for 2-d information processing. There are various formal methods for treating 2-d…

### Two-Dimensional Rational Automata: A Bridge Unifying One- and Two-Dimensional Language Theory

- Computer ScienceSOFSEM
- 2013

The model provides a uniform setting for the most important notions, techniques and results presented in the last decades for recognizable two-dimensional languages, and establishes new connections between one- and two- dimensional language theory.

### A note on identities of two-dimensional languages

- MathematicsDiscret. Appl. Math.
- 2005

### Two-dimensional pattern languages

- Computer ScienceNCMA
- 2013

Several classes of array languages obtained by generalising Angluin's pattern languages to the two-dimensional case are introduced and compared with respect to their expressive power and their closure properties are investigated.

### Recognizable vs. Regular Picture Languages

- Linguistics, Computer ScienceCAI
- 2007

The class of regular word languages plays a central role in formal language theory. Considerable effort has been made to transfer definitions and applications from word languages to their…

### Two-Dimensional Languages and Cellular Automata

- Computer ScienceInt. J. Found. Comput. Sci.
- 2012

It is shown that cellular automata whose two-dimensional languages are factorial-local have the same characterization as one-sided Cellular automata with SFT traces.

### Extending formal language hierarchies to higher dimensions

- Computer ScienceCSUR
- 1999

Two-dimensional languages defined (recognized, generated) by finite-state devices are described and definitions that are “natural extensions” from corresponding ones in the string theory are considered, where “ natural extension” has the precise meaning that, they reduce to the string case when restricted to pictures of one row (one column) only.

### On Two-Dimensional Pattern Matching by Finite Automata

- Computer ScienceCIAA
- 2005

The first of these two models presents an automata based version of the Bird and Baker approach with lower space complexity than the original algorithm, and a new model for two- dimensional approximate pattern matching using the two-dimensional Hamming distance is introduced.

### Higher Dimensional Automata

- Computer ScienceJ. Autom. Lang. Comb.
- 2004

It is provided the basics of a 2-dimensional theory of automata on series-parallel biposets and relates these classes to languages of series-Parallel bipOSets definable in monadic second-order logic.

### Regular Expressions and Context-Free Grammars for Picture Languages

- Computer ScienceSTACS
- 1997

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.

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