Computational Complexity of Segmentation

TL;DR

This paper analyzes the computational complexity of segmentation, revealing that formal assessments can challenge intuitive assumptions about its difficulty and search space, which are crucial for understanding cognitive and artificial systems.

Contribution

It provides the first formal complexity analysis of segmentation, demonstrating potential misconceptions in intuitive assumptions about its computational hardness.

Findings

Proves formal results on the hardness of segmentation

Shows search space size may be larger than intuition suggests

Challenges existing views on cognitive capacities

Abstract

Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the search space and complexity of a subcomputation. However, a mistaken intuition might make such initial conceptualizations misleading for what empirical questions appear relevant later on. We undertake here computational-level modeling and complexity analyses of segmentation - a widely hypothesized subcomputation that plays a requisite role in explanations of capacities across domains - as a case study to show how crucial it is to formally assess these assumptions. We mathematically prove two sets of results regarding hardness and search space size that may run counter to intuition, and position their implications with respect to existing views on the subcapacity.