The Hamiltonian path problem is one of the famous hard combinatorial problems. We provide the first molecular-scale autonomous solution of the decision Hamiltonian path problem. It is based on the formation of secondary structures of DNA molecules.
Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case. In this paper, we establish some connections between the two approaches. In particular, we show that the corresponding… (More)