The Program Is Still There: A Conservation Law for Program Discovery
A new paper introduces a conservation law for program discovery, suggesting that injecting structural knowledge into a search algorithm trades off directly against the search effort. This law quantifies the cost of finding the shortest program that generates a given sequence, showing that existing methods like Levin search and evolutionary algorithms have an exponential worst-case lower bound related to the search problem's coupling width. The research proposes an alternative approach that analyzes a candidate program's structure rather than just its score, which, while potentially incomplete for generic targets, demonstrated success in recovering generating programs for a significant portion of tested sequences, including elementary cellular automata. AI