Automata on Gauss Words

  • Alexei Lisitsa
  • Igor Potapov
  • Rafiq Saleh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5457)


In this paper we investigate the computational complexity of knot theoretic problems and show upper and lower bounds for planarity problem of signed and unsigned knot diagrams represented by Gauss words. Due to the fact the number of crossing in knots is unbounded, the Gauss words of knot diagrams are strings over infinite (unbounded) alphabet. For establishing the lower and upper bounds on recognition of knot properties we study these problems in a context of automata models over infinite alphabet.


Paired Word Euler Characteristic Jones Polynomial Input Word Data Word 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Alexei Lisitsa
    • 1
  • Igor Potapov
    • 1
  • Rafiq Saleh
    • 1
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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