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Decision Problems on Copying and Shuffling

Vesa Halava, Tero Harju, Dirk Nowotka, Esa Sahla

Abstract

We study decision problems of the form: given a regular or linear context-free language $L$, is there a word of a given fixed form in $L$, where given fixed forms are based on word operations copy, marked copy, shuffle and their combinations.

Decision Problems on Copying and Shuffling

Abstract

We study decision problems of the form: given a regular or linear context-free language , is there a word of a given fixed form in , where given fixed forms are based on word operations copy, marked copy, shuffle and their combinations.
Paper Structure (9 sections, 29 theorems, 16 equations)

This paper contains 9 sections, 29 theorems, 16 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Regular languages
  4. Powers and copies
  5. Shuffles
  6. Linear CF-languages
  7. Powers and copies
  8. Shuffles
  9. Conclusions

Key Result

Lemma 2.2

For a regular language $L$, there exists a natural number $p\ge 1$ such that, if $w \in L$ is of length $|w| \ge p$, then it has a factorization $w=xyz$ with $|y|\ge 1$ and $|xy|\le p$, such that $xy^nz \in L$ for all $n\in\mathbb{N}$.

Theorems & Definitions (33)

  • Example 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • Theorem 2.5
  • Theorem 3.1
  • Corollary 3.2
  • Lemma 3.3
  • Theorem 3.4
  • Theorem 3.5
  • ...and 23 more