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Soliton Automata Based on Trees

Soliton automata are a mathematical model for molecular switching devices. For even the simple case of soliton automata based on trees the behaviour is not known. For example, only two examples of such soliton automata were known the transition monoid of which is not the symmetric group on the set of states; and in these cases the transition monoid is the corresponding alternating group. We establish new bounds on the number of states of a tree-based soliton automaton and a sufficient condition for when the transition monoid of such a soliton automaton consists only of even permutations of the set of states. We also summarize the results of a systematic enumeration of tree-based soliton automata by which additional exceptions were found, each an alternating group in its natural representation.