Abstract
In this paper, we define a quasi-order on the set of read-once Boolean functions and show that this is a well-quasi-order. This implies that every parameter measuring complexity of the functions can be characterized by a finite set of minimal subclasses of read-once functions, where this parameter is unbounded. We focus on two parameters related to certificate complexity and characterize each of them in the terminology of minimal classes.
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Acknowledgements
Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST).
The authors are greatly indebted to anonymous reviewers for useful comments and suggestions, many of which have been incorporated in the text.
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Lozin, V., Moshkov, M. Critical Properties and Complexity Measures of Read-Once Boolean Functions. Ann Math Artif Intell 89, 595–614 (2021). https://doi.org/10.1007/s10472-021-09734-6
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DOI: https://doi.org/10.1007/s10472-021-09734-6