# On Some Recognizable Picture-Languages

@inproceedings{Reinhardt1998OnSR, title={On Some Recognizable Picture-Languages}, author={Klaus Reinhardt}, booktitle={MFCS}, year={1998} }

We show that the language of pictures over {a, b}, where all occurring b's are connected is recognizable, which solves an open problem in [Mat98]. We generalize the used construction to show that monocausal deterministically recognizable picture languages are recognizable, which is surprisingly nontrivial. Furthermore we show that the language of pictures over {a, b}, where the number of a's is equal to the number of b's is nonuniformly recognizable.

## 21 Citations

### The #a = #b Pictures Are Recognizable

- Computer ScienceSTACS
- 2001

It is shown that the language of pictures over {a,b} (with a reasonable relation between height and width) is recognizable using a finite tiling system, which means that counting in rectangular arrays is definable in existential monadic second-order logic.

### Recognizable Picture Series

- Computer ScienceJ. Autom. Lang. Comb.
- 2005

The quadrapolic automata weighted over a semiring compute picture series which have nice properties form a class of word series having properties similar to those of context-sensitive word languages.

### Ambiguity and Complementation in Recognizable Two-dimensional Languages

- Computer ScienceIFIP TCS
- 2008

The theory of one-dimensional (word) languages is well founded and investigated since fifties. From several years, the increasing interest for pattern recognition and image processing motivated the…

### Deterministically and Sudoku-Deterministically Recognizable Picture Languages

- Computer ScienceLATA
- 2007

It is shown that non-recognizable languages can be accepted by a generalization of this tiling system determinism which is called Sudoku-determinism, and even contains the set of 2-dimensional languages which can be recognized by 4-way alternating automata.

### 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…

### Restarting Automata for Picture Languages: A Survey on Recent Developments

- Computer ScienceCIAA
- 2014

Some recent developments obtained in a research project that aims at finding a deterministic model of a two-dimensional automaton that has the following desirable properties are presented.

### 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 Survey on Picture-Walking Automata

- Computer ScienceAlgebraic Foundations in Computer Science
- 2011

Survey results that compare the recognition power of different variants, consider their basic closure properties and study decidability questions are surveyed.

### Formal Language Characterizations of P, NP, and PSPACE

- Computer ScienceJ. Autom. Lang. Comb.
- 2008

The addition of one unbounded dimension for colouring leads to a characterization of PSPACE, the deterministic n-dimensional colourability of NP.

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