Molecular Switching by Turing Automata

We study the switching aspects of molecular computing from a novel algebraic point of view. Our approach is based on the concept indexed monoidal algebra, which provides an equivalent formalism for compact closed categories being used recently in the literature in connection with quantum computing. The point is to separate syntax, as the algebra G of graphs, from semantics, which is related to the algebra T of Turing automata, and define meaning as a homomorphism. Eventually, the syntax is restricted to the Gallai-Edmonds algebra G-E of graphs having a perfect internal matching, and the corresponding semantical structure, defined as the algebra S of soliton automata, is the quotient of an appropriate subalgebra of T .