Universal Sets and Cover-Free Families
Debjyoti Saharoy, Shailesh Vaya

TL;DR
This paper introduces a polynomial-time method to construct smaller universal sets over binary alphabets, significantly improving previous size bounds for applications in combinatorics and computer science.
Contribution
It presents a novel polynomial-time construction of $(n,d)$-universal sets with reduced size compared to prior methods, enhancing efficiency in related computational tasks.
Findings
Constructs $(n,d)$-universal sets of size $d imes 2^{d+o(d)} imes ext{log} n$
Achieves size reduction over previous bounds by Bshouty
Provides a polynomial-time algorithm for universal set construction
Abstract
We propose a polynomial time construction of an -universal set over alphabet , of size . This is an improvement over the size, , of an -universal set constructed by Bshouty, \cite{BshoutyTesters}, over alphabet .
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Taxonomy
Topicssemigroups and automata theory · Complexity and Algorithms in Graphs · graph theory and CDMA systems
