The Program Is Still There: A Conservation Law for Program Discovery
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 one less than the domain size. From it follows a conservation law: structural knowledge injected into a search trades one for one against the searc...
| Authors | Jorge Miguel Silva |
|---|---|
| Primary category | cs.CC |
| Published | 11 June 2026 |
| Last updated at source | 11 June 2026 |
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