Instruction sequence based non-uniform complexity classes

TL;DR

This paper introduces a novel approach to non-uniform complexity using instruction sequences, defining new classes analogous to P/poly and NP/poly, and explores their properties and conjectures.

Contribution

It presents a new framework for non-uniform complexity based on instruction sequences, including definitions of classes, completeness, and related conjectures.

Findings

Defined non-uniform complexity classes using instruction sequences

Introduced a notion of completeness for NP/poly-like classes

Formulated a conjecture analogous to NP not in P/poly

Abstract

We present an approach to non-uniform complexity in which single-pass instruction sequences play a key part, and answer various questions that arise from this approach. We introduce several kinds of non-uniform complexity classes. One kind includes a counterpart of the well-known non-uniform complexity class P/poly and another kind includes a counterpart of the well-known non-uniform complexity class NP/poly. Moreover, we introduce a general notion of completeness for the non-uniform complexity classes of the latter kind. We also formulate a counterpart of the well-known complexity theoretic conjecture that NP is not included in P/poly. We think that the presented approach opens up an additional way of investigating issues concerning non-uniform complexity.