document: Decomposition of additive cellular automata Finite additive cellular automata with fixed and periodic boundary conditions are considered as endomorphisms over pattern spaces . A characterization of the nilpotent and regular parts of these endomorphisms is given in terms of their minimal polynomials . Generalized eigenspace decomposition is determined and relevant cyclic subspaces are described in terms of symmetries . As an application , the lengths and frequencies of limit cycles in the transition diagram of the automaton are calculated
doc_bio_tags: O O O B I O O B I O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O
extractive_keyphrases: cellular automata transition diagram endomorphisms
abstractive_keyphrases: finite cellular automaton computational complexity