When Exponential Isn’t Inevitable: AI Refutes ETH

Some computer problems become brutally harder as they grow. The Exponential Time Hypothesis proposed that this explosion was unavoidable for a central logic problem called 3-SAT. OpenAI’s new result overturns that assumption with an algorithm that counts the solutions to fixed-width Boolean formulas in subexponential time, using polynomial space. We unpack what those words mean, why counting solutions also lets a computer decide whether one exists, and how the result reaches problems involving graph colorings and perfect matchings. We also separate this breakthrough from the still-open P versus NP question: subexponential does not mean polynomial, and a theoretical speedup is only the beginning of the search for practical algorithms. It is an exciting new invitation to reconsider where computing’s limits really lie. Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information. Sponsored by Embersilk LLC