Kolmogorov characterizations of complexity classes

Logical Characterizations of Complexity Classes

Kolmogorov-Loveland Sets and Advice Complexity Classes

Loveland complexity Loveland (1969) is a variant of Kolmogorov complexity, where it is asked to output separately the bits of the desired string, instead of the string itself. Similarly to the resource-bounded Kolmogorov sets we define Loveland sets. We highlight a structural connection between resource-bounded Loveland sets and some advice complexity classes. This structural connection enables...

Characterizations of Logarithmic Advice Complexity Classes

The complexity classes P=log and Full-P=log, corresponding to the two standard forms of logarithmic advice for polynomial time, are studied. The novel proof technique of \doubly exponential skip" is introduced, and characterizations for these classes are found in terms of several other concepts, among them easy-to-describe boolean circuits and reduction classes of tally sets with high regularit...

Unified characterizations of lowness properties via Kolmogorov complexity

Consider a randomness notion C. A uniform test in the sense of C is a total computable procedure that each oracle X produces a test relative to X in the sense of C. We say that a binary sequence Y is C-random uniformly relative to X if Y passes all uniform C tests relative to X. Suppose now we have a pair of randomness notions C and D where C ⊆ D, for instance Martin-Löf randomness and Schnorr ...

Recursion Theoretic Characterizations of Complexity Classes of Counting Functions

There has been a great eeort in giving machine independent, algebraic characterizations of complexity classes, especially of functions. Astonishingly, no satisfactory characterization of the prominent class # P has been known up to now. Here, we characterize # P as the closure of a set of simple arithmetical functions under summation and weak product. Building on that result, the hierarchy of c...