Finite state automata representing two-dimensional subshifts

Authors:
Nataša Jonoska;Joni B. Pirnot
Affiliations:
University of South Florida, Department of Mathematics, Tampa, FL;Manatee Community College, Department of Mathematics, Bradenton, FL
Venue:
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
Year:
2007

Citing 4
Cited 2

An introduction to symbolic dynamics and coding

An introduction to symbolic dynamics and coding
A small aperiodic set of Wang tiles

Discrete Mathematics
Recognizable picture languages and domino tiling

Theoretical Computer Science
Two-dimensional languages

Handbook of formal languages, vol. 3

On Complexity of Two Dimensional Languages Generated by Transducers

CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Transducer generated arrays of robotic nano-arms

Natural Computing: an international journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

We employ a two-dimensional automaton defined in [5] to recognize a class of two-dimensional shifts of finite type having the property that every admissable block found within the related local picture language can be extended to a point of the subshift. Here, we show that the automaton accurately represents the image of the represented two-dimensional shift of finite type under a block code. We further show that such automata can be used to check for a certain type of two-dimensional transitivity in the factor language of the corresponding shift space and how this relates to periodicity in the two-dimensional case. The paper closes with a notion of "follower sets" used to reduce the size of the automata representing two-dimensional sofic shifts.