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Bordered conjugates of words over large alphabets.

Harju, Tero; Nowotka, Dirk — 2008

The Electronic Journal of Combinatorics [electronic only]

The number of positions starting a square in binary words.

Harju, Tero; Kärki, Tomi; Nowotka, Dirk — 2011

The Electronic Journal of Combinatorics [electronic only]

On the periodicity of morphisms on free monoids

Tero Harju; Matti Linna — 1986

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Density of critical factorizations

Tero Harju; Dirk Nowotka — 2002

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We investigate the density of critical factorizations of infinite sequences of words. The density of critical factorizations of a word is the ratio between the number of positions that permit a critical factorization, and the number of all positions of a word. We give a short proof of the Critical Factorization Theorem and show that the maximal number of noncritical positions of a word between two critical ones is less than the period of that word. Therefore, we consider only words of index one,...

Undecidability of the equivalence of finite substitutions on regular language

Vesa Halava; Tero Harju — 1999

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Towards a characterization of bipartite switching classes by means of forbidden subgraphs

Jurriaan Hage; Tero Harju — 2007

Discussiones Mathematicae Graph Theory

We investigate which switching classes do not contain a bipartite graph. Our final aim is a characterization by means of a set of critically non-bipartite graphs: they do not have a bipartite switch, but every induced proper subgraph does. In addition to the odd cycles, we list a number of exceptional cases and prove that these are indeed critically non-bipartite. Finally, we give a number of structural results towards proving the fact that we have indeed found them all. The search for critically...

Undecidability of infinite post correspondence problem for instances of Size 9

Vesa Halava; Tero Harju — 2006

RAIRO - Theoretical Informatics and Applications

In the infinite Post Correspondence Problem an instance consists of two morphisms and , and the problem is to determine whether or not there exists an infinite word such that . This problem was shown to be undecidable by Ruohonen (1985) in general. Recently Blondel and Canterini ( (2003) 231–245) showed that this problem is undecidable for domain alphabets of size 105. Here we give a proof that the infinite Post Correspondence Problem is undecidable for instances where the morphisms...

Undecidability of the equivalence of finite substitutions on regular language

Vesa Halava; Tero Harju — 2010

RAIRO - Theoretical Informatics and Applications

A simplified proof is given for the following result due to Lisovik: it is undecidable for two given –free finite substitutions, whether they are equivalent on the regular language {0,1} .

Density of Critical Factorizations

Tero Harju; Dirk Nowotka — 2010

RAIRO - Theoretical Informatics and Applications

The theorem of Fine and Wilf for relational periods

Vesa Halava; Tero Harju; Tomi Kärki — 2009

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider relational periods, where the relation is a compatibility relation on words induced by a relation on letters. We prove a variant of the theorem of Fine and Wilf for a (pure) period and a relational period.

The theorem of Fine and Wilf for relational periods

Vesa Halava; Tero Harju; Tomi Kärki — 2008

RAIRO - Theoretical Informatics and Applications

On the number of squares in partial words

Vesa Halava; Tero Harju; Tomi Kärki — 2010

RAIRO - Theoretical Informatics and Applications

The theorem of Fraenkel and Simpson states that the maximum number of distinct squares that a word of length can contain is less than . This is based on the fact that no more than two squares can have their last occurrences starting at the same position. In this paper we show that the maximum number of the last occurrences of squares per position in a partial word containing one hole is , where is the size of the alphabet. Moreover, we prove that the number of distinct squares in a partial word...

Equality sets for recursively enumerable languages

Vesa Halava; Tero Harju; Hendrik Jan Hoogeboom; Michel Latteux — 2005

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider shifted equality sets of the form $E_{G} (a, g_{1}, g_{2}) = {w ∣ g_{1} (w) = a g_{2} (w)}$ , where $g_{1}$ and $g_{2}$ are nonerasing morphisms and $a$ is a letter. We are interested in the family consisting of the languages $h (E_{G} (J))$ , where $h$ is a coding and $E_{G} (J)$ is a shifted equality set. We prove several closure properties for this family. Moreover, we show that every recursively enumerable language $L \subseteq A^{*}$ is a projection of a shifted equality set, that is, $L = π_{A} (E_{G} (a, g_{1}, g_{2}))$ for some (nonerasing) morphisms $g_{1}$ and $g_{2}$ and a letter $a$ , where $π_{A}$ deletes the letters not in $A$ . Then we deduce...

Equality sets for recursively enumerable languages

Vesa Halava; Tero Harju; Hendrik Jan Hoogeboom; Michel Latteux — 2010

RAIRO - Theoretical Informatics and Applications

We consider shifted equality sets of the form , where and are nonerasing morphisms and is a letter. We are interested in the family consisting of the languages , where is a coding and is a shifted equality set. We prove several closure properties for this family. Moreover, we show that every recursively enumerable language is a projection of a shifted equality set, that is, for some (nonerasing) morphisms and and a letter...

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Currently displaying 1 – 14 of 14

Bordered conjugates of words over large alphabets.

The number of positions starting a square in binary words.

On the periodicity of morphisms on free monoids

Density of critical factorizations

Undecidability of the equivalence of finite substitutions on regular language

Towards a characterization of bipartite switching classes by means of forbidden subgraphs

Undecidability of infinite post correspondence problem for instances of Size 9

Undecidability of the equivalence of finite substitutions on regular language

Density of Critical Factorizations

The theorem of Fine and Wilf for relational periods

The theorem of Fine and Wilf for relational periods

On the number of squares in partial words

Equality sets for recursively enumerable languages

Equality sets for recursively enumerable languages