28

This would be analogous to the Kolmogorov complexity of a string, except that in this case, I'm interested in the algorithm that solves a given problem using the least number of steps.

We would therefore have to be able to show that any other algorithm is at best of the same order of complexity as the algorithm in question.

I'm asking because I'm working on a paper that makes use of this concept, and I was surprised when I realized that I'm not aware of any name for this concept, though I'll concede I'm risking embarrassment if there is such a name that I'm simply unaware of.

Raphael
  • 73,212
  • 30
  • 182
  • 400
Feynmanfan85
  • 383
  • 3
  • 7

2 Answers2

35

You can say that an algorithm is asymptotically optimal in such a case.

In general, people might also say that an algorithm is optimal in some other sense, like assuming some particular complexity-theoretic conjecture like (S)ETH.

Juho
  • 22,905
  • 7
  • 63
  • 117
3

I've seen this concept explained as Solomonoff induction, a formalization of Occam's razor.

Given some set of Turing machines that fit the data, the one with the lowest complexity is likely to be the one that truly models it.

Bill Mei
  • 131
  • 4