Turing Automata and Graph Machines

TL;DR

This paper introduces indexed monoidal algebras as an equivalent framework for self-dual compact closed categories, and generalizes Turing machines into Turing automata and graph machines, proposing reversible computational models inspired by data-flow architecture.

Contribution

It establishes a new algebraic framework for Turing automata and graph machines, enabling reversible computation models and a molecular hardware example.

Findings

Indexed monoidal algebras are equivalent to self-dual compact closed categories.

Turing graph machines can serve as reversible universal computational devices.

A molecular size hardware model exemplifies reversible computation.

Abstract

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.