What is a POLYNOMIAL-TIME Computable L2-Function?

TL;DR

This paper explores two natural definitions of polynomial-time computability for L2 functions and demonstrates their fundamental incomparability under certain complexity class assumptions.

Contribution

It introduces and compares two natural definitions of polynomial-time computability for L2 functions, revealing their fundamental differences.

Findings

The two definitions are incomparable unless FP_1 includes #P_1.

Provides a formal framework for polynomial-time computability of L2 functions.

Highlights complexity-theoretic implications of these definitions.

Abstract

We give two natural definitions of polynomial-time computability for L2 functions; and we show them incomparable (unless complexity class FP_1 includes #P_1).