Discrete mathematics
Newton's method for the matrix square root
Mathematics of Computation
Introduction to algorithms
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Computing roots of graphs is hard
Discrete Applied Mathematics
A Padé Approximation Method for Square Roots of Symmetric Positive Definite Matrices
SIAM Journal on Matrix Analysis and Applications
On the Sequence of Consecutive Powers of a Matrix in a Boolean Algebra
SIAM Journal on Matrix Analysis and Applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
SIAM Journal on Discrete Mathematics
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We show that finding roots of Boolean matrices is an NP-hard problem. This answers a 20 year old question from semigroup theory. Interpreting Boolean matrices as directed graphs, we further reveal a connection between Boolean matrix roots and graph isomorphism, which leads to a proof that for a certain subclass of Boolean matrices related to subdivision digraphs, root finding is of the same complexity as the graph-isomorphism problem.