Randomness conservation inequalities; information and independence in mathematical theories
Information and Control
Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Computability
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Complexity theory of real functions
Complexity theory of real functions
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Computability on the probability measures on the Borel sets of the unit interval
Theoretical Computer Science - Special issue on computability and complexity in analysis
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Computable analysis: an introduction
Computable analysis: an introduction
Randomness as an Invariant for Number Representations
Proceedings of the Colloquium in Honor of Arto Salomaa on Results and Trends in Theoretical Computer Science
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Connectivity Properties of Dimension Level Sets
Electronic Notes in Theoretical Computer Science (ENTCS)
Randomness with Respect to the Signed-Digit Representation
Fundamenta Informaticae
Computability of probability measures and Martin-Löf randomness over metric spaces
Information and Computation
Applications of Effective Probability Theory to Martin-Löf Randomness
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
An Application of Martin-Löf Randomness to Effective Probability Theory
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
Information and Computation
Randomness and the ergodic decomposition
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Randomness with Respect to the Signed-Digit Representation
Fundamenta Informaticae
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Following a suggestion of Zvonkin and Levin, we generalize Martin-Löf's definition of infinite random sequences over a finite alphabet via randomness tests to effective topological spaces with a measure. We show that under weak computability conditions there is a universal randomness test. We prove a theorem on randomness preserving functions which corrects and extends a result by Schnorr and apply it to a number of examples. In particular, we show that a real number is random if, and only if, it has a random b- ary representation, for any b ≥ 2. We show that many computable, continuously differentiable real functions preserve randomness. Especially, all computable analytic functions which are not constant on any open subset of their domain preserve randomness. Finally, we introduce a new randomness concept for subsets of natural numbers, which we characterize in terms of random sequences. Surprisingly, it turns out that there are infinite co-r.e. random sets.