Measuring Bias Through Optimal Search Time

Given an optimal problem solver such as OOPS, problem $r$, current code bias $q_{0:a_{frozen}}$, the most recent start address $a_{last}$, and information about the starts and ends of previously frozen programs $q^1,q^2,\ldots,q^k$, the total search time $T(r,q^1,q^2,\ldots,q^k,a_{last},a_{frozen})$ for solving $r$ can be used to define the degree of bias

$$B(r,q^1,q^2,\ldots,q^k,a_{last},a_{frozen}) := 1 / T(r,q^1,q^2,\ldots,q^k,a_{last},a_{frozen}).$$

The smaller the bias, the longer the search time of any bias-optimal searcher. Compare the concept of conceptual jump size (Solomonoff, [69,70]).

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