• Corpus ID: 3147866

On Operations Preserving Primitivity of Partial Words with One Hole

  title={On Operations Preserving Primitivity of Partial Words with One Hole},
  author={F. Blanchet-Sadri and Sarah A. Nelson and Amelia Tebbe},
The notion of a primitive word, one that is not a power of another word, is useful in many areas including coding theory, combinatorics on words, formal language theory, and text algorithms. The proportion of such words turns out to be very high. We investigate operations that preserve the primitivity of partial words with one hole, or words that have an undefined position. As a result, all primitive binary partial words with on e hole of length up to 11 can be generated. 
2 Citations
On Del-Robust Primitive Partial Words with One Hole
A special class of words is characterized, del-robust primitive partial words with one hole, that remains primitive on deletion of any symbol or the hole, and it is proved that the language of non-del-robUST primitive partial Words with one Hole is not context-free.
On Exchange-Robust and Subst-Robust Primitive Partial Words
It is shown that the language of non-exchangerobust primitive partial words is not context-free over a binary alphabet and of substituting a symbol by another symbol from the alphabet.


Testing primitivity on partial words
A linear time algorithm to test primitivity on partial words, which are strings that may contain a number of ''do not know'' symbols, based on the combinatorial result that under some condition, a partial word is primitive if and only if it is not compatible with an inside factor of its square.
Some operations preserving primitivity of words
The operations are chosen in such a way that in the case of a two-letter alphabet, all primitive words of length @?11 can be obtained from single letters.
Counting Primitive Partial Words
The number of primitive partial words, which are strings that may contain “do not know” symbols, is investigated.
Word insertions and primitivity ∗
In this paper we consider relations between the operation of word insertion and primitivity. A necessary and sufficient condition under which the insertion u ← u of the word u into itself has maximum
Primitive partial words
Some fundamental results about primitive words are extended to primitive partial words, which are strings that may have a number of ''do not know'' symbols.
Algorithmic Combinatorics on Partial Words
This paper focuses on two areas of algorithmic combinatorics on partial words, namely, pattern avoidance and subword complexity, and discusses recent contributions as well as a number of open problems.
On the Language of Primitive Words
  • H. Petersen
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1996
It is proved that the set Q of primitive words over an alphabet is not an unambiguous context-free language and the same holds for the set L of Lyndon words, which implies efficient decidability on the RAM model of computation.
Primitive Morphisms
  • V. Mitrana
  • Computer Science, Mathematics
    Inf. Process. Lett.
  • 1997
A precise characterization of primitive morphisms is provided in terms of pure codes and an easily testable characterization is given for uniform morphisms over the binary alphabet.
On the robustness of primitive words
This work investigates the effect on primitive words of point mutations, of morphisms, and of the operation of taking prefixes, and several ways of producing primitive words are obtained.
Partial Words and a Theorem of Fine and Wilf
A variant of Fine and Wilf's theorem for partial words is proved, and extensions of some general combinatorial properties of words are given.