• Corpus ID: 39597453

Ins-Robust Primitive Words

@article{Srivastava2017InsRobustPW,
  title={Ins-Robust Primitive Words},
  author={Amit Kumar Srivastava and Kalpesh Kapoor},
  journal={ArXiv},
  year={2017},
  volume={abs/1707.01010}
}
Let Q be the set of primitive words over a finite alphabet with at least two symbols. We characterize a class of primitive words, Q_I, referred to as ins-robust primitive words, which remain primitive on insertion of any letter from the alphabet and present some properties that characterizes words in the set Q_I. It is shown that the language Q_I is dense. We prove that the language of primitive words that are not ins-robust is not context-free. We also present a linear time algorithm to… 

References

SHOWING 1-10 OF 14 REFERENCES

On del-robust primitive words

The Ambiguity of Primitive Words

It is proved that the set Q of primitive words over an alphabet is not an unambiguous context-free language and it is shown that the same holds for the set L of Lyndon words.

Formal Languages Consisting of Primitive Words

It is proved that Q has two rather strong context-free-like properties: the first is that Q satisfies the nonempty, strong variant of Bader and Moura's iteration condition, and the second is that intersecting Q with any member of a special, infinite family of regular languages, the authors get a context- free language.

Primitive words and roots of words

An overview about relevant research to this topic during the last twenty years including own investigations and some new results is given and several generalizations of the notions of periodicity and primitivity of words are dedicated.

On Maximal Repetitions in Words

It is proved that the maximal number of maximal repetitions in general words (on arbitrary alphabet) of length n is linearly-bounded in n, and some applications and consequences are mentioned.

The Language of Primitive Words in not Regular: Two Simple Proofs

Two simple proofs are given to show that the language Q of all primitive words over a nontrivial alphabet is not regular and of well-known sublanguages of Q.

Finding maximal repetitions in a word in linear time

  • R. KolpakovG. Kucherov
  • Mathematics
    40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
  • 1999
This work proves a combinatorial result asserting that the sum of exponents of all maximal repetitions of a word of length n is bounded by a linear function in n, which implies that there is only a linear number of maximal repetition in a word.

On the robustness of primitive words

Combinatorics on Words

  • T. Harju
  • Computer Science, Mathematics
  • 2004
Words (strings of symbols) are fundamental in computer processing, and nearly all computer software use algorithms on strings.