An Application of the Deutsch-Jozsa Algorithm to Formal Languages and the Word Problem in Groups

  • Michael Batty
  • Andrea Casaccino
  • Andrew J. Duncan
  • Sarah Rees
  • Simone Severini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5106)

Abstract

We adapt the Deutsch-Jozsa algorithm to the context of formal language theory. Specifically, we use the algorithm to distinguish between trivial and nontrivial words in groups given by finite presentations, under the promise that a word is of a certain type. This is done by extending the original algorithm to functions of arbitrary length binary output, with the introduction of a more general concept of parity. We provide examples in which properties of the algorithm allow to reduce the number of oracle queries with respect to the deterministic classical case. This has some consequences for the word problem in groups with a particular kind of presentation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Michael Batty
    • 1
  • Andrea Casaccino
    • 2
  • Andrew J. Duncan
    • 1
  • Sarah Rees
    • 1
  • Simone Severini
    • 3
  1. 1.Department of MathematicsUniversity of Newcastle upon TyneUnited Kingdom
  2. 2.Information Engineering DepartmentUniversity of SienaItaly
  3. 3.Institute for Quantum Computing and Department of Combinatorics and OptimizationUniversity of WaterlooCanada

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