Abstract
For non-uniform cellular automata (NUCA) over an arbitrary universe with multiple local transition rules, we introduce and investigate fundamental dynamical properties such as stable injectivity, stable reversibility, and stable post-surjectivity. Over infinite amenable group universes (e.g. infinite abelian groups), we show that it is impossible to obtain injective NUCA by disturbing the local transition rules of a finite number of cells of non-injective cellular automata. Moreover, we establish the equivalence between reversibility, stable reversibility, and stable injectivity for NUCA. The surjectivity and invertibility of several classes of injective and stably injective NUCA are also obtained.
Published Version
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.
