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Comparative Analysis of Deterministic and Nondeterministic Decision Trees for Decision Tables from Closed Classes.
Azimkhon Ostonov1, Mikhail Moshkov1
1Computer, Electrical and Mathematical Sciences & Engineering Division and Computational Bioscience Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia.
Entropy (Basel, Switzerland)
|June 26, 2024
Summary
This study examines decision tables with many-valued decisions, analyzing complexity relationships between tables and decision trees. Seven distinct relationship types were identified, offering insights into computational complexity.
Area of Science:
- Computer Science
- Information Systems
- Decision Analysis
Background:
- Decision tables are crucial for representing complex decision-making processes.
- Understanding the complexity of decision tables and their corresponding decision trees is vital for efficient algorithm design.
- Previous research has explored various aspects of decision table optimization, but relationships between table complexity and decision tree complexity remain an active area of study.
Purpose of the Study:
- To investigate the relationships among three key parameters: decision table complexity, minimum deterministic decision tree complexity, and minimum nondeterministic decision tree complexity.
- To analyze classes of decision tables that are closed under specific operations (column removal, decision change, column permutation, column duplication).
- To classify the functions that characterize these relationships and identify all possible types of such relationships.
Main Methods:
- Consideration of specific classes of many-valued decision tables closed under defined operations.
- Analysis of three complexity parameters: decision table complexity (number of columns), minimum deterministic decision tree complexity, and minimum nondeterministic decision tree complexity.
- Application of rough classification to functions characterizing the relationships between these parameters.
Main Results:
- Identification and enumeration of all seven possible types of relationships between the studied complexity parameters.
- Characterization of decision table classes based on their closure properties under column and decision operations.
- Demonstration of how different operations affect the complexity landscape of decision tables and associated decision trees.
Conclusions:
- The study establishes a comprehensive classification of relationships between decision table and decision tree complexities.
- The findings provide a theoretical framework for understanding and potentially optimizing decision table representations.
- The identified seven relationship types offer valuable insights for researchers and practitioners in areas like artificial intelligence and software engineering.
Keywords:
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