A 2 O(n) TIME ALGORITHM FOR 3-SAT [pdf] (hexagonmath.org)

Claude's research team has unveiled a groundbreaking deterministic algorithm for the 3-SAT problem that operates in time 2o(n), effectively challenging the long-held Exponential Time Hypothesis (ETH). This development is particularly significant as 3-SAT is a foundational NP-complete problem, and the new algorithm not only solves 3-SAT but also counts the number of satisfying assignments for #3-SAT, positioning it as a step forward in understanding computational limits. Previous methods faced exponential time complexities, with the best-known deterministic algorithms operating in O(1.328n) time. The implications of this result extend beyond 3-SAT; it suggests that many other NP-complete problems, such as Independent Set and Clique, can be addressed more efficiently, running in time O(2δn) for any δ > 0. While this algorithm demonstrates theoretical advancements in computational complexity, it also indicates that existing assumptions in the field, such as ETH and its stronger counterpart, the Strong Exponential Time Hypothesis (SETH), may need reevaluation. However, the algorithm's practical applications are limited, as it does not provide immediate solutions for real-world NP-complete problems, particularly for sizes much smaller than n = 10^1000.