On the complexity of Boolean matrix ranks
Yaroslav Shitov
TL;DR
This paper proves that computing the fooling set number and the determinantal rank of a Boolean matrix is NP-hard, highlighting the computational difficulty of these matrix properties.
Contribution
It introduces a reduction demonstrating the NP-hardness of determining fooling set number and determinantal rank in Boolean matrices.
Findings
Fooling set number is NP-hard to compute.
Determinantal rank is NP-hard to compute.
Establishes computational complexity of these matrix measures.
Abstract
We construct a reduction which proves that the fooling set number and the determinantal rank of a Boolean matrix are NP-hard to compute.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · semigroups and automata theory · Algorithms and Data Compression