  Indexed monoidal algebras are introduced as an equivalent structure for
self-dual compact closed categories, and a coherence theorem is proved for the
category of such algebras. Turing automata and Turing graph machines are
defined by generalizing the classical Turing machine concept, so that the
collection of such machines becomes an indexed monoidal algebra. On the analogy
of the von Neumann data-flow computer architecture, Turing graph machines are
proposed as potentially reversible low-level universal computational devices,
and a truly reversible molecular size hardware model is presented as an
example.
