On the length of knot transformations via reidemeister moves i and II

Authors:
Rafiq Saleh
Affiliations:
Department of Computer Science, University of Liverpool, Liverpool, U.K.
Venue:
RP'12 Proceedings of the 6th international conference on Reachability Problems
Year:
2012

Citing 4
Cited 0

Term rewriting and all that

Term rewriting and all that
Towards Regular Languages over Infinite Alphabets

MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Planarity of knots, register automata and logspace computability

LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
On notions of regularity for data languages

FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

Knots are defined as embeddings of a circle in 3-dimensional Euclidean space, but can be faithfully represented by finite structures, such as graphs or words. One of such discrete representations is a Gauss code. In this paper we consider knot transformations in terms of string rewriting systems. We formulate the concept of knot transformations in the context of Gauss word rewriting and present linear lower and upper bounds on the length of knot transformations for the equivalence problem of two knot diagrams reachable by a sequence of Reidemeister moves of type I and II.