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We developed an efficient incremental algorithm for learning Deterministic Finite Automata (DFA) using inverse queries. This new method reduces computational complexity, improving DFA learning for complex systems.

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Area of Science:

  • Computer Science
  • Theoretical Computer Science
  • Machine Learning

Background:

  • Deterministic Finite Automata (DFA) are fundamental in theoretical computer science and pattern recognition.
  • Existing incremental learning algorithms for DFAs can have high time complexity, limiting their application to complex systems.
  • The Identification of Regular Languages (ID) algorithm provides a foundation for DFA learning but requires adaptation for incremental settings.

Purpose of the Study:

  • To present an efficient incremental learning algorithm for Deterministic Finite Automata (DFA).
  • To reduce the time complexity of incremental DFA learning compared to existing methods.
  • To ensure convergence to a minimal DFA representation with finite labeled examples.

Main Methods:

  • The study introduces the Incremental DFA Learning algorithm through Inverse Queries (IDLIQ).
  • This algorithm extends the Identification of Regular Languages (ID) algorithm to an incremental learning setup.
  • It utilizes labeled examples, membership queries (MQ), and inverse queries (IQ) posed to a minimally adequate teacher (MAT).

Main Results:

  • The IDLIQ algorithm achieves a reduced time complexity (from cubic to square) in the presence of a MAT.
  • The algorithm constructs a hypothesis automaton consistent with all observed examples and IQ responses.
  • Convergence to a minimal DFA representation is ensured with a finite number of labeled examples.

Conclusions:

  • The IDLIQ algorithm offers a more efficient approach to incremental DFA learning.
  • The reduced complexity makes it more suitable for learning large and complex systems.
  • The correctness and termination of the IDLIQ algorithm have been formally proven.