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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Veröffentlicht in:Annals of mathematics and artificial intelligence Jg. 89; H. 5-6; S. 595 - 614
Hauptverfasser: Lozin, Vadim, Moshkov, Mikhail
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.06.2021
Springer
Springer Nature B.V
Schlagworte:
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
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-021-09734-6