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 in:Annals of mathematics and artificial intelligence Vol. 89; no. 5-6; pp. 595 - 614
Main Authors: Lozin, Vadim, Moshkov, Mikhail
Format: Journal Article
Language:English
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
ISSN:1012-2443, 1573-7470
Online Access:Get full text
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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