The Fastest and Shortest Algorithm for All Well-Defined Problems

• Published in 2002
• Added on 2012-08-14

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.

Links

• http://www.hutter1.net/ai/pfastprg.htm
• http://arxiv.org/abs/cs.CC/0206022
• https://arxiv.org/pdf/cs/0206022.pdf

Other information

BibTeX entry

@article{Hutter2002,
	key = {Hutter2002},
	type = {article},
	title = {The Fastest and Shortest Algorithm for All Well-Defined Problems},
	author = {Hutter, Marcus},
	abstract = {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. 

},
	comment = {},
	date_added = {2012-08-14},
	date_published = {2002-12-07},
	urls = {http://www.hutter1.net/ai/pfastprg.htm,http://arxiv.org/abs/cs.CC/0206022,https://arxiv.org/pdf/cs/0206022.pdf},
	collections = {Attention-grabbing titles,Basically computer science},
	url = {http://www.hutter1.net/ai/pfastprg.htm http://arxiv.org/abs/cs.CC/0206022 https://arxiv.org/pdf/cs/0206022.pdf},
	urldate = {2012-08-14},
	year = 2002,
	journal = {International Journal of Foundations of Computer Science},
	keywords = {Kolmogorov complexity,acceleration,algorithmic information theory,blum's speed-up theorem,computational complexity,levin search},
	number = 3,
	pages = {431--443},
	volume = 13
}