Abstract
Global functions of cellular automata on state spaces equipped with the Cantor topology are well characterized by the Curtis–Hedlund–Lyndon theorem. In this paper, we develop a characterization of global functions of cellular automata on Z , if the state space is equipped by Weyl and Besicovitch topology. The necessary and sufficient condition for a function to be the global map of a cellular automaton is (1) a strong localization property, a condition that strengthen Lipschitz continuity, (2) the set of (Cantor) periodic states are positively invariant and (3) the function commutes (in the Weyl/Besicovitch sense) with the shift operator.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
