Abstract
Sensitivity, block sensitivity, and certificate complexity are complexity measures for Boolean functions. In this paper, we prove that these three complexity measures are equal to each other if a Boolean function is a unate function or a read-once function. We also prove \(\sqrt{n}\) tight lower bounds for the three complexity measures of read-once functions. As an application of our results, the decision tree complexity of unate functions and read-once functions is upper bounded by the square of the sensitivity of the function.
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Morizumi, H. (2014). Sensitivity, Block Sensitivity, and Certificate Complexity of Unate Functions and Read-Once Functions. In: Diaz, J., Lanese, I., Sangiorgi, D. (eds) Theoretical Computer Science. TCS 2014. Lecture Notes in Computer Science, vol 8705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44602-7_9
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DOI: https://doi.org/10.1007/978-3-662-44602-7_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44601-0
Online ISBN: 978-3-662-44602-7
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