# Unambiguous recognizable two-dimensional languages

@article{Anselmo2006UnambiguousRT, title={Unambiguous recognizable two-dimensional languages}, author={Marcella Anselmo and Dora Giammarresi and Maria Madonia and Antonio Restivo}, journal={RAIRO Theor. Informatics Appl.}, year={2006}, volume={40}, pages={277-293} }

We consider the family UREC of unambiguous recognizable two-dimensional languages. We prove that there are recognizable languages that are inherently ambiguous, that is UREC family is a proper subclass of REC family. The result is obtained by showing a necessary condition for unambiguous recognizable languages. Further UREC family coincides with the class of picture languages defined by unambiguous 2OTA and it strictly contains its deterministic counterpart. Some closure and non-closure…

## 55 Citations

### Classes of two-dimensional languages and recognizability conditions

- Computer ScienceRAIRO Theor. Informatics Appl.
- 2010

It is shown that all the known necessary conditions for recognizability of a language and its complement are not sufficient, and a necessary condition for Recognizability stated by Matz is reformed, introducing a new complexity function.

### A Note on Unambiguity, Finite Ambiguity and Complementation in Recognizable Two-Dimensional Languages

- Computer ScienceCAI
- 2009

The paper gives partial answers based on the introduction of special classes of languages of "high complexity", in a sense specified in the paper and motivated by some necessary conditions holding for recognizable and unambiguous languages.

### Deterministic and Unambiguous Families within Recognizable Two-dimensional Languages

- Computer ScienceFundam. Informaticae
- 2010

The notion of deterministic tiling system and the corresponding family of languages (DREC) and its structural and closure properties are introduced and it is shown that, in contrast with the one-dimensional case, there exist other classes between deterministic and non-deterministic families.

### A Brief Excursion Inside the Class of Tiling Recognizable Two-Dimensional Languages

- Computer ScienceDevelopments in Language Theory
- 2010

It is shown that some definitions of unambiguity are equivalent to corresponding notions of determinism and therefore correspond decidable classes closed under complementation and linear parsing algorithms.

### Tiling Recognizable Two-Dimensional Languages

- Computer ScienceCAI
- 2007

The notion of deterministic and unambiguous tiling system that generalizes deterministicand unambiguous automata for strings is introduced and it is shown that, differently from the one-dimensional case, there exist other distinct classes besides deterministic, unambiguous and non-deterministic families that can be separated by means of examples and decidability properties.

### A Stronger Recognizability Condition for Two-dimensional Languages

- Computer ScienceDiscret. Math. Theor. Comput. Sci.
- 2013

The paper presents a condition necessarily satisfied by (tiling system) recognizable two-dimensional languages, which is compared with all the other ones known in the literature and results to be the strongest one, while the remaining ones are its particular cases.

### Exploring inside Tiling Recognizable Picture Languages to Find Deterministic subclasses

- Computer ScienceInt. J. Found. Comput. Sci.
- 2011

It is shown that some definitions of unambiguity are equivalent to particular notions of determinism and therefore the corresponding REC subclasses have linear parsing algorithms and are closed under complementation.

### Comparing Necessary Conditions for Recognizability of Two-Dimensional Languages

- Computer ScienceCAI
- 2011

This paper focuses on two known conditions necessarily satisfied by a recognizable language, that are based on the idea to reduce the problem from picture to string languages, and states a new necessary condition for the recognizability of two-dimensional languages.

### Communication complexity tools on recognizable picture languages

- Computer Science, LinguisticsTheor. Comput. Sci.
- 2019

### Deterministic and unambiguous two-dimensional languages over one-letter alphabet

- Computer ScienceTheor. Comput. Sci.
- 2009

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