Multi-dimensional fast rule filter automata

Group-valued multi-dimensional filter automata fulfilling a set of neighbor hood axioms are considered and a corresponding extended Fast Rule Theorem ( FRT) is derived. These automata comprise the well known reversible and irre versible parity rule filter automata with solitonic behavior in one dimensi on. The extended fast rule gives rise to a scanning algorithm with inherent parallel structure (pipelining parallelism). Those automata which suffice the extended fast rule theorem are completely characterized in terms of loc al configuration functions. In contrast to the one-dimensional case, in sev eral dimensions the FRT does not generally imply solitonic behavior. Theref ore, examples of solitonic and non-solitonic collisions for particles in tw o-dimensional automata are given. (C) 1999 Elsevier Science B.V. All rights reserved.