Computing a Knot Invariant as a Constraint Satisfaction Problem

Details Computing a Knot Invariant as a Constraint Satisfaction Problem Computing a Knot Invariant as a Constraint Satisfaction Problem

2011-11-04

arxiv.org/abs/1111.1060v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 3 figures, submitted to short note in Journal of Physical Society of Japan

Scientific paper

We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides an algorithm to find the solution. The method also allows one to get some deeper insight into the structural complexity of knots, which is expected to be related with the landscape structure of constraint satisfaction problem.

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