Self-Specifying Machines

TL;DR

This paper explores self-specifying machines, revealing their computational power aligns with certain reductions to NP and P sets, and discusses conditions under which these classes coincide.

Contribution

It introduces the concept of self-specifying machines and characterizes their language acceptance power through reductions to NP and P sets, linking it to complexity class equalities.

Findings

Self-specifying machines accept languages reducible to NP and P sets.

The classes coincide if and only if a specific complexity class equality holds.

The work connects machine self-specification with classical complexity class relationships.

Abstract

We study the computational power of machines that specify their own acceptance types, and show that they accept exactly the languages that $\manyonesharp$-reduce to NP sets. A natural variant accepts exactly the languages that $\manyonesharp$-reduce to P sets. We show that these two classes coincide if and only if $\psone = \psnnoplusbigohone$, where the latter class denotes the sets acceptable via at most one question to $\sharpp$ followed by at most a constant number of questions to $\np$.