2 research outputs found
STATE-OF-ART Algorithms for Injectivity and Bounded Surjectivity of One-dimensional Cellular Automata
Surjectivity and injectivity are the most fundamental problems in cellular
automata (CA). We simplify and modify Amoroso's algorithm into optimum and make
it compatible with fixed, periodic and reflective boundaries. A new algorithm
(injectivity tree algorithm) for injectivity is also proposed. After our
theoretic analysis and experiments, our algorithm for injectivity can save much
space and 90\% or even more time compared with Amoroso's algorithm for
injectivity so that it can support the decision of CA with larger neighborhood
sizes. At last, we prove that the reversibility with the periodic boundary and
global injectivity of one-dimensional CA is equivalent