Search problems in vector spaces

Heger Tamas; Patkos Balazs; Takats Marcella

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Search problems in vector spaces

机译：向量空间中的搜索问题

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摘要

We consider the following -analog of the basic combinatorial search problem: let be a prime power and the finite field of elements. Let denote an -dimensional vector space over and let be an unknown 1-dimensional subspace of . We will be interested in determining the minimum number of queries that is needed to find provided all queries are subspaces of and the answer to a query is YES if and NO if . This number will be denoted by in the adaptive case (when for each queries answers are obtained immediately and later queries might depend on previous answers) and in the non-adaptive case (when all queries must be made in advance). In the case we prove if is large enough. While for general values of and we establish the bounds and provided tends to infinity.

机译：我们考虑以下基本组合搜索问题的类比：设为素数和元素的有限域。让表示上的一维向量空间，让成为的未知一维子空间。如果所有查询都是的子空间，并且查询的答案为YES（是）和NO（如果），我们将对确定查找所需的最小查询数感兴趣。在自适应情况下（当每个查询都立即获得答案，以后的查询可能取决于先前的答案时），在非自适应情况下（必须提前进行所有查询时），该数字将由表示。在这种情况下，我们证明是否足够大。而对于和的一般值，我们确定范围并提供趋向于无穷大。

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来源
《Designs, Codes and Crytography》 |2015年第2期|207-216|共10页
作者
Heger Tamas; Patkos Balazs; Takats Marcella;
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作者单位

MTA ELTE Geometr & Algebra Combinator Res Grp, H-1117 Budapest, Hungary;

MTA ELTE Geometr & Algebra Combinator Res Grp, H-1117 Budapest, Hungary|Hungarian Acad Sci, Alfred Renyi Inst Math, H-1364 Budapest, Hungary;

Eotvos Lorand Univ, Dept Comp Sci, H-1117 Budapest, Hungary;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Combinatorial search; Q-analog; Projective space; Separating system;

机译：组合搜索;Q模拟;投影空间;分离系统;

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Search problems in vector spaces

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