Deciding the deterministic property for soliton graphs

Soliton automata are a mathematical model for electronic switching at the molecular level. In the design of soliton circuits, deterministic automata are of primary importance. The underlying graphs of such automata, called soliton grahs, are characterized in terms of generalized trees and graphs having a unique perfect matching. Based on this characterization, a modification of the currently most efficient unique perfect matching algorithm is worked out to decide in O(mlog4n) time if a graph with n vertices and m edges defines a deterministic soliton automaton. A yet more efficient O(m) algorithm is given for the special case of chestnut and elementary soliton graphs. All of these algorithms are capable of constructing a state for the corresponding soliton automaton found, and the general algorithm can also be used to simplify the automaton to an isomorphic elementary one.