Knot Coloring as Verification

Abstract

This work presents the CMK knot coloring software system. CMK is a command-line tool written in SWI-Prolog that computes colorings of three-dimensional knots by finite quandles. The original purpose was to classify knots by certain computational properties. CMK features a predicate that computes knot quandle presentations from braid words. The authors describe the key algorithms. Errors in five braid representations within the Mathematica™ KnotData collection are revealed through CMK.