arXiv:2606.13799v1 Announce Type: cross Abstract: Finding the shortest program that generates a sequence is uncomputable, and for six decades that fact has been mistaken for a wall around finding any generating program. It is not a wall but a price, and this paper measures it. For every algorithm that learns about a candidate program only through its score, a class spanning Levin search, evolutionary methods, simulated annealing, and the cross-entropy method, we define the coupling width of a search problem and prove an unconditional worst-case lower bound, exponential in that width with base
This paper represents a significant theoretical breakthrough in understanding the fundamental limits and possibilities of program discovery, building on six decades of foundational computer science.
A strategic reader should care because this research reframes the perceived 'uncomputability' of program discovery into a measurable 'price,' potentially opening new avenues for designing more effective AI systems for automated code generation and discovery.
The understanding of program discovery is shifting from an intractable problem to one with quantifiable costs and constraints, which could guide future research and development in AI for code generation.
- · AI researchers
- · Machine learning engineers
- · Software development tools
- · Developers relying solely on brute-force search methods
This paper provides theoretical underpinnings for the design of more efficient and targeted AI program discovery algorithms.
Improved program discovery could accelerate software development and the creation of specialized AI agents.
More efficient program generation might lead to AI systems that can autonomously fix or optimize their own code or even generate novel algorithms for complex problems.
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Read at arXiv cs.LG