منابع مشابه
Irredundant Families of Subcubes
We consider the problem of finding the maximum possible size of a family of k-dimensional subcubes of the n-cube {0, 1}n, none of which is contained in the union of the others. (We call such a family ‘irredundant’). Aharoni and Holzman [1] conjectured that for k > n/2, the answer is ( n k ) (which is attained by the family of all k-subcubes containing a fixed point). We give a new proof of a ge...
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In this paper, we consider tolerances induced by irredundant coverings. Each tolerance R on U determines a quasiorder .R by setting x .R y if and only if R(x) ⊆ R(y). We prove that for a tolerance R induced by a covering H of U , the covering H is irredundant if and only if the quasiordered set (U,.R) is bounded by minimal elements and the tolerance R coincides with the product &R ◦.R. We also ...
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It is shown that every uncountable Boolean algebra A contains an uncountable subset / such that no a of / is in the subalgebra generated by I\{a} using an additional axiom of set theory. It is also shown that a use of some such axiom is necessary. A subset / of a Boolean algebra A is irredundant if no proper subset of / generates the same subalgebra as /, or equivalently, if no a of / is in the...
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A new approach to Boolean decomposition and matching is proposed. It uses enumeration of all support-reducing decompositions of Boolean functions up to 16 inputs. The approach is implemented in a new framework that compactly stores multiple circuit structures. The method makes use of pre-computations performed offline, before the framework is started by the calling application. As a result, the...
متن کاملIrredundant Generating Sets of Finite Nilpotent Groups
It is a standard fact of linear algebra that all bases of a vector space have the same cardinality, namely the dimension of the vector space over its base field. If we treat a vector space as an additive abelian group, then this is equivalent to saying that an irredundant generating set for a vector space must have cardinality equal to the dimension of the vector space. The same is not true for...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2014
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2013.08.012