An order-preserving property of additive invariants for Takesue-type reversible cellular automata
We show that, for a large and important class of reversible, one-dimensional cellular automata, the set of additive invariants exhibits an algebraic structure. More precisely, if f and gate one-dimensional, reversible cellular automata of the kind considered by Takesue (1989) [1], we show that the component-wise maximum boolean OR on these automata is such that psi(f) subset of psi(f boolean OR g), where psi(f) denotes the set of additive invariants of f and subset of denotes the inclusion relation between real subspaces. (C) 2010 Elsevier B.V. All rights reserved.
invariants reversibility cellular automata conserved quantities noether's theorem elementary reversible cellular automata (erca) discrete dynamical systems