Musings on generic-case complexity

TL;DR

This paper introduces a broader definition of generic-case complexity by employing a random process to generate inputs and measuring input size based on the generation time, enhancing the understanding of algorithm performance on typical cases.

Contribution

It presents a novel, more general framework for generic-case complexity that incorporates input generation time as a measure of input size, expanding previous definitions.

Findings

Provides a new definition of generic-case complexity

Uses input generation time as a size metric

Lays groundwork for analyzing algorithms with randomized inputs

Abstract

We propose a more general definition of generic-case complexity, based on using a random process for generating inputs of an algorithm and using the time needed to generate an input as a way of measuring the size of that input.