# Unambiguous 1-uniform morphisms

@article{Nevisi2011Unambiguous1M, title={Unambiguous 1-uniform morphisms}, author={Hossein Nevisi and Daniel A. Reidenbach}, journal={Theor. Comput. Sci.}, year={2011}, volume={478}, pages={101-117} }

A morphism @s is unambiguous with respect to a word @a if there is no other morphism @t that maps @a to the same image as @s. In the present paper we study the question of whether, for any given word, there exists an unambiguous 1-uniform morphism, i.e., a morphism that maps every letter in the word to an image of length 1.

## 3 Citations

### Unambiguous 1-Uniform Morphisms (cid:73)

- Mathematics
- 2012

A morphism σ is unambiguous with respect to a word α if there is no other morphism τ that maps α to the same image as σ . In the present paper we study the question of whether, for any given word,…

### Morphic Primitivity and Alphabet Reductions

- Mathematics, Computer ScienceDevelopments in Language Theory
- 2012

The present paper investigates the effect of alphabet reductions on morphically primitive words, i.e., words that are not a fixed point of a nontrivial morphism and answers a question on the existence of unambiguous alphabet reductions for such words.

### Institutional Repository Morphic primitivity and alphabet reductions

- Mathematics, Computer Science
- 2017

The present paper investigates the effect of alphabet reductions on morphically primitive words, i.

## References

SHOWING 1-10 OF 18 REFERENCES

### Weakly Unambiguous Morphisms

- MathematicsSTACS
- 2011

The main result is a compact characterisation that holds for all morphisms with ternary or larger target alphabets, and comprehensively describes those words that have a weakly unambiguous length-increasing morphism with a unary target alphabet.

### On a conjecture about finite fixed points of morphisms

- MathematicsTheor. Comput. Sci.
- 2005

### Unambiguous erasing morphisms in free monoids

- MathematicsRAIRO Theor. Informatics Appl.
- 2010

The present paper demonstrates that, in contrast to the main result by Freydenberger et al., the existence of an unambiguous erasing morphisms for a given string can essentially depend on the size of the target alphabet of the morphism.

### Unambiguous Morphic Images of Strings

- MathematicsDevelopments in Language Theory
- 2005

The studies demonstrate that the existence of unambiguous morphic images essentially depends on the structure of α, and formulates the main result according to which a string α can be mapped by an injective morphism onto an unambiguous image if and only if α is succinct.

### The Unambiguity of Segmented Morphisms

- MathematicsDevelopments in Language Theory
- 2007

This work features the first approach to a characterisation of sets of strings with respect to which certain fixed morphisms are unambiguous, and it leads to fairly counter-intuitive insights into the relations between such sets.