Complexity of Deterministic and Strongly Nondeterministic Decision Trees for Decision Tables From Closed Classes

This paper investigates classes of decision tables (DTs) with 0-1-decisions that are closed under the removal of attributes (columns) and changes to the assigned decisions to rows. For tables from any closed class (CC), the authors examine how the minimum complexity of deterministic decision trees (...

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Bibliographic Details
Published in:IEEE access Vol. 12; pp. 164979 - 164988
Main Authors: Ostonov, Azimkhon, Moshkov, Mikhail
Format: Journal Article
Language:English
Published: Piscataway IEEE 2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Boolean functions
Closed classes of decision tables
Complexity
Complexity theory
Data analysis
Decision trees
deterministic decision trees
Fault diagnosis
Greedy algorithms
Object recognition
Optimization
Polynomials
Risk management
strongly nondeterministic decision trees
ISSN:2169-3536, 2169-3536
Online Access:Get full text
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Summary:This paper investigates classes of decision tables (DTs) with 0-1-decisions that are closed under the removal of attributes (columns) and changes to the assigned decisions to rows. For tables from any closed class (CC), the authors examine how the minimum complexity of deterministic decision trees (DDTs) depends on the minimum complexity of a strongly nondeterministic decision tree (SNDDT). Let this dependence be described with the function <inline-formula> <tex-math notation="LaTeX">F_{\Psi ,A}(n) </tex-math></inline-formula>. The paper establishes a condition under which the function <inline-formula> <tex-math notation="LaTeX">F_{\Psi , A}(n) </tex-math></inline-formula> can be defined for all values. Assuming <inline-formula> <tex-math notation="LaTeX">F_{\Psi , A}(n) </tex-math></inline-formula> is defined everywhere, the paper proved that this function exhibits one of two behaviors: it is bounded above by a constant or it is at least n for infinitely many values of n. In particular, the function <inline-formula> <tex-math notation="LaTeX">F_{\Psi , A}(n) </tex-math></inline-formula> can grow as an arbitrary nondecreasing function <inline-formula> <tex-math notation="LaTeX">\varphi (n) </tex-math></inline-formula> that satisfies <inline-formula> <tex-math notation="LaTeX">\varphi (n) \geq n </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\varphi ({0}) = 0 </tex-math></inline-formula>. The paper also provided conditions under which the function <inline-formula> <tex-math notation="LaTeX">F_{\Psi , A}(n) </tex-math></inline-formula> remains bounded from above by a polynomial in n.
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ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2024.3487514