On the Complexity and Decidability of Some Problems Involving Shuffle

  • Joey Eremondi
  • Oscar H. Ibarra
  • Ian McQuillanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9118)


The complexity and decidability of various decision problems involving the shuffle operation (denoted by Open image in new window ) are studied. The following three problems are all shown to be \(\mathsf{NP}\)-complete: given a nondeterministic finite automaton (\(\mathsf{NFA}\)) \(M\), and two words \(u\) and \(v\), is Open image in new window , is Open image in new window , and is Open image in new window ? It is also shown that there is a polynomial-time algorithm to determine, for \(\mathsf{NFA}\)s \(M_1, M_2\) and a deterministic pushdown automaton \(M_3\), whether Open image in new window . The same is true when \(M_1, M_2,M_3\) are one-way nondeterministic \(l\)-reversal-bounded \(k\)-counter machines, with \(M_3\) being deterministic. Other decidability and complexity results are presented for testing whether given languages \(L_1, L_2\) and \(L\) from various languages families satisfy Open image in new window .


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Joey Eremondi
    • 1
  • Oscar H. Ibarra
    • 2
  • Ian McQuillan
    • 3
    Email author
  1. 1.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  3. 3.Department of Computer ScienceUniversity of SaskatchewanSaskatoonCanada

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