Abstraction/Representation Theory for Heterotic Physical Computing

TL;DR

This paper introduces a rigorous theoretical framework for understanding how physical computing devices interact with abstract computation through representation relations, enabling formal analysis of hybrid and heterotic computing systems.

Contribution

It develops a formal abstraction/representation theory that links physical devices and abstract computation, with conditions for their interaction and implications for hybrid computing.

Findings

Framework establishes conditions for representation and device theory to produce commuting diagrams.

Addresses hybrid computing and distinguishes heterotic from hybrid systems.

Provides a basis for formal analysis of nonstandard physical computers.

Abstract

We give a rigorous framework for the interaction of physical computing devices with abstract computation. Device and program are mediated by the non-logical 'representation relation'; we give the conditions under which representation and device theory give rise to commuting diagrams between logical and physical domains, and the conditions for computation to occur. We give the interface of this new framework with currently existing formal methods, showing in particular its close relationship to refinement theory, and the implications for questions of meaning and reference in theoretical computer science. The case of hybrid computing is considered in detail, addressing in particular the example of an internet-mediated 'social machine', and the abstraction/representation framework used to provide a formal distinction between heterotic and hybrid computing. This forms the basis for future use of the framework in formal treatments of nonstandard physical computers.