Computer Science – Computational Complexity
Scientific paper
2002-06-14
International Journal of Foundations of Computer Science, Vol.13, No.3, June 2002, 431-443
Computer Science
Computational Complexity
12 pages, 1 figure
Scientific paper
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 low-order 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 $f$.
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