Cellular automata with vanishing particles

Issue title: Cellular Automata

Article type: Research Article

Authors: Kůrka, Petr

Affiliations: Faculty of Mathematics and Physics, Charles University in Prague, Malostranské náměstí 25, CZ-11800 Praha 1, Czech Republic

Abstract: We consider particle weight functions which assign weights to certain words. Given a cellular automaton, we search for particle weight functions, for which the total weights of configurations do not increase with time. In this case the weight of a shift-invariant Borel probability measure does not increase either, so we get a Ljapunov function on the space of measures. We give some conditions which ensure that the weight of a measure converges to zero. In particular we prove that this happens in the elementary cellular automaton rule number 18 and in a variant of the Gacs-Kurdyumov-Levin cellular automaton.

Keywords: cellular automata, particles, Borel probability measures, invariant subshifts

Journal: Fundamenta Informaticae, vol. 58, no. 3-4, pp. 203-221, 2003