共查询到20条相似文献,搜索用时 31 毫秒
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A real x is called h-bounded computable , for some function h:N→N, if there is a computable sequence (xs) of rational numbers which converges to x such that, for any n∈N, at most h(n) non-overlapping pairs of its members are separated by a distance larger than 2-n. In this paper we discuss properties of h-bounded computable reals for various functions h. We will show a simple sufficient condition for a class of functions h such that the corresponding h-bounded computable reals form an algebraic field. A hierarchy theorem for h-bounded computable reals is also shown. Besides we compare semi-computability and weak computability with the h-bounded computability for special functions h. 相似文献
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Taisuke Izumi Akinori Saitoh Toshimitsu Masuzawa 《Journal of Parallel and Distributed Computing》2007
The Δ-timed uniform consensus is a stronger variant of the traditional consensus and it satisfies the following additional property: every correct process terminates its execution within a constant time Δ (Δ-timeliness), and no two processes decide differently (uniformity). In this paper, we consider the Δ-timed uniform consensus problem in presence of fc crash processes and ft timing-faulty processes, and propose a Δ-timed uniform consensus algorithm. The proposed algorithm is adaptive in the following sense: it solves the Δ-timed uniform consensus when at least ft+1 correct processes exist in the system. If the system has less than ft+1 correct processes, the algorithm cannot solve the Δ-timed uniform consensus. However, as long as ft+1 processes are non-crashed, the algorithm solves (non-timed) uniform consensus. We also investigate the maximum number of faulty processes that can be tolerated. We show that any Δ-timed uniform consensus algorithm tolerating up to ft timing-faulty processes requires that the system has at least ft+1 correct processes. This impossibility result implies that the proposed algorithm attains the maximum resilience about the number of faulty processes. We also show that any Δ-timed uniform consensus algorithm tolerating up to ft timing-faulty processes cannot solve the (non-timed) uniform consensus when the system has less than ft+1 non-crashed processes. This impossibility result implies that our algorithm attains the maximum adaptiveness. 相似文献
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We prove an explicit bound on the radius of a ball centered at the origin which is guaranteed to contain all bounded connected components of a semi-algebraic set S⊂Rk defined by a weak sign condition involving s polynomials in Z[X1,…,Xk] having degrees at most d, and whose coefficients have bitsizes at most τ. Our bound is an explicit function of s,d,k and τ, and does not contain any undetermined constants. We also prove a similar bound on the radius of a ball guaranteed to intersect every connected component of S (including the unbounded components). While asymptotic bounds of the form 2τdO(k) on these quantities were known before, some applications require bounds which are explicit and which hold for all values of s,d,k and τ. The bounds proved in this paper are of this nature. 相似文献
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We formalize paper fold (origami) by graph rewriting. Origami construction is abstractly described by a rewriting system (O,?), where O is the set of abstract origamis and ? is a binary relation on O, that models fold . An abstract origami is a structure (Π,∽,?), where Π is a set of faces constituting an origami, and ∽ and ? are binary relations on Π, each representing adjacency and superposition relations between the faces. 相似文献