Simulation Complexity

Article type: Research Article

Authors: Hay, Nicholas J.

Affiliations: Centre for Discrete Mathematics and Computer Science, University of Auckland, New Zeland. E-mail: nickhay@cs.auckland.ac.nz

Abstract: In Algorithmic Information Theory, the algorithmic complexity of a sequence is the length of the shortest program which generates it. Is there a measure of the complexity of a computer? We define the simulation complexity of a computer to be the least cost of simulating that computer on a fixed universal computer. We generalise this to processes, computers which can have potentially infinite output (e.g. monotone Turingmachines). Thismeasure has monotone complexity as a special case. Simulation complexity has applications to sequence prediction, leading to a clarification of a central prediction error inequality and a stronger form of dominance. Enumerable semimeasures are functions which represent sequence predictors. These semimeasures can be in turn represented by processes. A universal process generates a universal semimeasure: one that outperforms any other predictor but for a cost depending on how complex that predictor is. This extra cost is exactly the simulation complexity of the predictor.

Journal: Fundamenta Informaticae, vol. 83, no. 1-2, pp. 117-140, 2008