Abstract Storage Devices

TL;DR

This paper introduces the concept of abstract storage devices (ASDs) to model quantum-like storage with partial read capabilities, analyzing their properties, equivalences, and computational complexities.

Contribution

It formalizes ASDs as a combinatorial abstraction, explores their structural properties, and establishes complexity results for their reduction, equivalence, and factorization.

Findings

Every ASD has an equivalent minimal-state ASD.

Reducibility of ASDs is NP-complete.

Device equivalence is at least as hard as graph isomorphism.

Abstract

A quantum storage device differs radically from a conventional physical storage device. Its state can be set to any value in a certain (infinite) state space, but in general every possible read operation yields only partial information about the stored state. The purpose of this paper is to initiate the study of a combinatorial abstraction, called abstract storage device (ASD), which models deterministic storage devices with the property that only partial information about the state can be read, but that there is a degree of freedom as to which partial information should be retrieved. This concept leads to a number of interesting problems which we address, like the reduction of one device to another device, the equivalence of devices, direct products of devices, as well as the factorization of a device into primitive devices. We prove that every ASD has an equivalent ASD with minimal number of states and of possible read operations. Also, we prove that the reducibility problem for ASD's is NP-complete, that the equivalence problem is at least as hard as the graph isomorphism problem, and that the factorization into binary-output devices (if it exists) is unique.