Detecting Unknots via Equational Reasoning, I: Exploration

  • Andrew Fish
  • Alexei Lisitsa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8543)


We explore the application of automated reasoning techniques to unknot detection, a classical problem of computational topology. We adopt a two-pronged experimental approach, using a theorem prover to try to establish a positive result (i.e. that a knot is the unknot), whilst simultaneously using a model finder to try to establish a negative result (i.e. that the knot is not the unknot). The theorem proving approach utilises equational reasoning, whilst the model finder searches for a minimal size counter-model. We present and compare experimental data using the involutary quandle of the knot, as well as comparing with alternative approaches, highlighting instances of interest. Furthermore, we present theoretical connections of the minimal countermodels obtained with existing knot invariants, for all prime knots of up to 10 crossings: this may be useful for developing advanced search strategies.


Fundamental Group Homomorphic Image Automate Reasoning Automate Theorem Prove Automate Deduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Andrew Fish
    • 1
  • Alexei Lisitsa
    • 2
  1. 1.School of Computing, Engineering and MathematicsUniversity of BrightonUK
  2. 2.Department of Computer ScienceThe University of LiverpoolUK

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