Critical Properties and Complexity Measures of Read-Once Boolean Functions

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 i...

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Bibliographic Details
Published inAnnals of mathematics and artificial intelligence Vol. 89; no. 5-6; pp. 595 - 614
Main Authors Lozin, Vadim, Moshkov, Mikhail
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2021
Springer
Springer Nature B.V
Subjects
Artificial Intelligence
Boolean
Boolean functions
Codes
Complex Systems
Complexity
Computer Science
Game theory
Graphs
Mathematics
Measurement
Parameters
Terminology
06E30
Certificate complexity
Well-quasi-ordering
Read-once Boolean function
06A07
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Summary: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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ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-021-09734-6