Abstract

Motivated by the search for idempotent cellular automata (CA), we study CA that act almost as the identity unless they read a fixed pattern p. We show that constant and symmetrical patterns always generate idempotent CA, and we characterize the quasi-constant patterns that generate idempotent CA. Our results are valid for CA over an arbitrary group G. Moreover, we study the semigroup theoretic natural partial order defined on idempotent CA. If G is infinite, we prove that there is an infinite independent set of idempotent CA, and if G has an element of infinite order, we prove that there is an infinite increasing chain of idempotent CA.

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 call

Disclaimer: 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.