Computational Complexity of Segmentation
This work addresses foundational issues in computational modeling for researchers in cognitive science and AI, though it is incremental in applying formal analysis to a specific subcomputation.
The paper tackles the problem of unexamined intuitive assumptions about the computational complexity of segmentation in cognitive systems, proving mathematical results on hardness and search space size that challenge these assumptions.
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.