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Soliton-like dynamics of filtrons of cyclic automata

Iteration of certain automata mappings performed over a string of symbols reveals some soliton-like coherent entities. These discrete solitons are called filtrons of automata. They were first discovered (and called particles) in binary strings for parity rule filter cellular automata (CAs) by Park, Steiglitz and Thurston. Since then, further models based on filter CAs capable of supporting the filtrons have been proposed. There are soliton CAs, fast rules, ultradiscrete soliton equations, integrable CAs, filter transducers, crystal models and box-ball systems among them. In this paper we apply a unified automaton description for such discrete soliton-supporting systems. We show a wide class of cyclic automata, so-called filter automata (FAs), that support the filtrons. FAs generalize some of the models mentioned above. For FAs we present a technique called ring computation, a kind of inverse method. This computation applies inverse FAs and an edge description of a filtron. Our technique is aimed at predicting the existence of a filtron that could be supported by a given FA. We present various filtrons and quasi-filtrons supported by automata, especially the family of automata that is equivalent to box-ball system with a carrier.