An extractor is a function that receives some randomness and either “improves” it or produces “new” randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov extractors and modify it to resourcebounded version of Kolmogorov complexity. Following Zimand we prove the existence of such objects with certain parameters. The uti...

We now prove Theorem 1. Let M be a probabilistic machine running in space S (and time 2S), using R random bits, and deciding a language L with two-sided error. (Note that S, R are functions of the input length n, and the theorem requires S = Ω(log n).) We will assume without loss of generality that M always uses exactly R random bits on all inputs. Fixing an input x and letting ` be some parame...

This paper investigates the computational power of space-bounded quantum Turing machines. The following facts are proved for space-constructible space bounds s satisfying s(n) = Ω(log n). 1. Any quantum Turing machine (QTM) running in space s can be simulated by an unbounded error probabilistic Turing machine (PTM) running in space O(s). No assumptions on the probability of error or running tim...

AMERICANS are taught that the English Unitarian minister Joseph Priestley discovered oxygen in 1774. Scandinavians are taught that the Swedish apothecary Carl Wilhelm Scheele generated oxygen in Uppsala in 1771–2, several years before Priestley. Scheele claimed that he wrote Lavoisier, describing the experiments in September, 1774. However, Lavoisier denied seeing or receiving his letter. Among...

in this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the hypercyclicity criterion. we characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional banach space .

We prove that the category of left-handed skew distributive lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a noncommutative version of classical Priestley duality for distributive lattices. The result also generalizes the recent development of Stone duality for skew Boolean algebras.

In this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the Hypercyclicity Criterion. We characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional Banach space .