Kekulé Cells for Molecular Computation

The configurations of single and double bonds in polycyclic hydrocarbons are abstracted as Kekulé states of graphs. Sending a socalled soliton over an open channel between ports (external nodes) of the graph changes the Kekulé state and therewith the set of open channels in the graph. This switching behaviour is proposed as a basis for molecular computation. The proposal is highly speculative but may have tremendous impact. Kekulé states with the same boundary behaviour (port assignment) can be regarded as equivalent. This gives rise to the abstraction of Kekulé cells. The basic theory of Kekulé states and Kekulé cells is developed here, up to the classification of Kekulé cells with ≤ 4 ports. To put the theory in context, we generalize Kekulé states to semi-Kekulé states, which form the solutions of a linear system of equations over the field of the bits 0 and 1. We briefly study so-called omniconjugated graphs, in which every port assignment of the right signature has a Kekulé state. Omniconjugated graphs may be useful as connectors between computational elements. We finally investigate some examples with potentially useful switching behaviour.