Physical Computation, P/poly and P/log*

TL;DR

This paper introduces a framework for classical physical computation systems without randomness or error, showing their polynomial-time capabilities align with complexity classes P/poly and P/log*.

Contribution

It develops a novel framework for physical computation, characterizing classical systems' computational power as equivalent to P/poly and P/log* in polynomial time.

Findings

Physical systems can compute within P/poly and P/log*

Measurement and transformation times can vary with input

Framework extends to error-free classical physical computation

Abstract

In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities in polynomial time are equivalent to P/poly. We then extend our framework to describe how measurement and transformation times may vary depending on their input. Finally we describe two classes of classical "physical" computation systems in this new framework whose computational capabilities in polynomial time are equivalent to P/poly and P/log*.