Abstract
This special issue of Theory of Computing Systems contains articles which relate to talks given at the 8th International Conference on Computability, Complexity and Randomness (CCR) in Moscow from the 23rd to the 27th of September 2015. The CCR conference series is devoted to algorithmic randomness, Kolmogorov complexity, and their relationship with computability theory, complexity theory, logic and reverse mathematics. The contributions to this special issue reflect both the interests of reserachers in Russia, in particular Kolmogorov and computational complexity, and new directions in the field of algorithmic randomness such as the focus on normal numbers and connections to ergodic theory. No conference proceedings have been published; this special issue is the only publication relating to the confernece. All contributions are a significant extension of the conference presentations, and underwent the usual rigorous journal reviewing process. The article Polynomial-time algorithms for checking some properties of Boolean functions given by polynomials by Svetlana Selezneva and Anton Bukhman presents a polynomial time algorithm, which tests whether a Boolean function represented by a multivariate polynomial over GF(2) is even, that is, has zero derivative in the direction of (1, . . . , 1). The approach is based on the notion of the characteristic of monomials in the polynomial representation of Boolean functions. In Normality and finite-state dimension of Liouville numbers Satyadev Nandakumar gives a new construction of a Liouville number which is normal for a given base. Vladimir V’yugin in On Stability of Probability Laws with Respect to Small Violations of Algorithmic Randomness examines the robustness of ergodic theorems when the assumption of randomness is relaxed only a little. For example he shows that
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