(for example, by a mathematical expression of reasonable size) are by definition not Kolmogorov random. Further, within the set of all possible objective functions, levels of goodness are equally represented among candidate solutions, hence good solutions are scattered throughout the space of candidates. Accordingly, a search algorithm will rarely evaluate more than a small fraction of the candidates before locating a very good solution. Almost all objective functions are of such high Kolmogorov complexity that they cannot be stored in a particular computer. More precisely, if we model a given physical computer as a register machine with a given size memory on the order of the memories of modern computers, then most objective functions cannot be stored in their memories. There is more information in the typical objective function or algorithm than Seth Lloyd estimates the observable universe is capable of registering. For instance, if each candidate solution is encoded as a sequence of 300 0's and 1's, and the goodness values are 0 and 1, then most objective functions have Kolmogorov complexity of at least 2300 bits, and this is greater than Lloyd's bound of 1090 ≈ 2299 bits. It follows that the original "no free lunch" theorem does not apply to what can be stored in a physical computer; instead the so-called "tightened" no free lunch theorems need to be applied. It has also been shown that NFL results apply to incomputable functions. Formal synopsis is the set of all objective functions f:X→Y, where is a finite solution space and is a finite poset. The set of all permutations of X is J. A random variable F is distributed on . For all j in J, F o j is a random variable distributed on , with P(F o j = f) = P(F = f o j−1) for all f in . Let a(f) denote the output of search algorithm a on input f. If a(F) and b(F) are identically distributed for all search algorithms a and b, then F has an NFL distribution. This condition holds if and only if F and F o j are identically distributed for all j in J. In other words, there is no free lunch for search algorithms if and only if the distribution of objective functions is invariant under permutation of the solution space. Set-theoretic NFL theorems have recently been generalized to arbitrary cardinality and . Origin Wolpert and