The Fastest and Shortest Algorithm for All Well-Defined Problems

An algorithm M is described that solves any well-defined problem p as quickly as the fastest algorithm computing a solution to p, save for a factor of 5 and loworder additive terms. M optimally distributes resources between the execution of provably correct p-solving programs and an enumeration of all proofs, including relevant proofs of program correctness and of time bounds on program runtimes. M avoids Blum's speed-up theorem by ignoring programs without correctness proof. M has broader applicability and can be faster than Levin's universal search, the fastest method for inverting functions save for a large multiplicative constant. An extension of Kolmogorov complexity and two novel natural measures of function complexity are used to show that the most efficient program computing some function f is also among the shortest programs provably computing f. 1 Published in the International Journal of Foundations of Computer Science, Vol. 13, No. 3, (June 2002) 431

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Marcus Hutter
• Keywords: Algorithms, CORR 2002, Correct P-solving Programs, Education, Loworder Additive Terms