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Decision Trees for Binary Subword-Closed Languages.

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.

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Summary
This summary is machine-generated.

This study analyzes decision tree depths for binary subword-closed languages. Findings reveal distinct growth patterns for recognition and membership problems, classifying languages into five complexity classes.

Keywords:
deterministic decision treemembership problemnondeterministic decision treerecognition problemsubword-closed language

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Area of Science:

  • Theoretical Computer Science
  • Formal Languages and Automata Theory
  • Computational Complexity

Background:

  • Subword-closed languages are a class of formal languages with specific structural properties.
  • Decision trees are fundamental data structures used for solving recognition and membership problems.
  • Understanding the complexity of these problems is crucial for efficient language processing.

Purpose of the Study:

  • To investigate the minimum depth of decision trees for recognition and membership problems in binary subword-closed languages.
  • To analyze the deterministic and nondeterministic complexities of these problems.
  • To classify binary subword-closed languages based on the growth of decision tree depths.

Main Methods:

  • Analysis of decision tree depths for deterministic and nondeterministic recognition.
  • Analysis of decision tree depths for deterministic and nondeterministic membership testing.
  • Comparison of growth rates of minimum tree depths with respect to word length 'n'.
  • Identification of complexity classes based on joint behavior of tree depths.

Main Results:

  • Deterministic recognition tree depth is constant, logarithmic, or linear in 'n'.
  • Nondeterministic recognition and both deterministic/nondeterministic membership tree depths are constant or linear in 'n'.
  • Five distinct complexity classes of binary subword-closed languages are identified based on these depth behaviors.

Conclusions:

  • The depth of decision trees for these problems exhibits predictable growth patterns.
  • These patterns allow for a robust classification of binary subword-closed languages into complexity classes.
  • The findings contribute to a deeper understanding of the computational complexity of formal languages.