Planarity of knots, register automata and logspace computability

Authors:
Alexei Lisitsa;Igor Potapov;Rafiq Saleh
Affiliations:
Department of Computer Science, University of Liverpool, Liverpool, UK;Department of Computer Science, University of Liverpool, Liverpool, UK;Department of Computer Science, University of Liverpool, Liverpool, UK
Venue:
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Year:
2011

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Abstract

In this paper we investigate the complexity of planarity of knot diagrams encoded by Gauss words, both in terms of recognition by automata over infinite alphabets and in terms of classical logarithmic space complexity. As the main result, we show that recognition of planarity of unsigned Gauss words can be done in deterministic logarithmic space and by deterministic register automata. We also demonstrate generic results on the mutual simulations between logspace bounded classical computations (over finite alphabets) and register automata working over infinite alphabets.