A real number x is absolutely normal if, for every base b≥2, two equally long strings of digits appear with equal asymptotic frequency in the base-b expansion x. This paper presents an explicit algorithm that generates binary x, nth bit appearing after npolylog(n) computation steps. speed achieved by simultaneously computing and diagonalizing against a martingale incorporates Lempel-Ziv parsing...

Inconsistencies frequently occur in news about the real-world. Some of these inconsistencies may be more significant than others, and some news may contain more inconsistencies than others. This creates problems of deciding whether to act on these inconsistencies, and if so how. Possible actions on an inconsistency in a news report include ignore the inconsistency, resolve the inconsistency, an...

In [10] Osorio et al. introduced a paraconsistent three-valued logic, the logic CG3 which was named after the logic G ′ 3 due to the close relation between them. Authors defined CG3 via the three-valued matrix that defines G3 but changing the set of designated truth values. In this article we present a brief study of the Kripke-type semantics for some logics related with CG3 before constructing...

In this work we present additional results related to the property of strong equivalence of logic programs. This property asserts that two programs share the same set of stable models, even under the addition of new rules. As shown in a recent work by Lifschitz, Pearce and Valverde, strong equivalence can be simply reduced to equivalence in the logic of Here-and-There (HT). In this paper we pro...

A b s t r a c t. The paper deals with functional properties of three-valued logics. We consider the family of regular three-valued Kleene's logics (strong, weak, intermediate) and it's extensions by adding an implicative connectives (" natural " implications). The main result of our paper is the lattice that describes the relations between implicative extensions of regular logics. In this paper...