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Automata Learning: An Algebraic Approach

Published: 08 July 2020 Publication History

Abstract

We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of languages and their recognizing algebraic structures. Using the concept of an automata presentation of T-algebras, we demonstrate that the task of learning a T-recognizable language can be reduced to learning an abstract form of algebraic automaton whose transitions are modeled by a functor. For the important case of adjoint automata, we devise a learning algorithm generalizing Angluin's L*. The algorithm is phrased in terms of categorically described extension steps; we provide for a termination and complexity analysis based on a dedicated notion of finiteness. Our framework applies to structures like ω-regular languages that were not within the scope of existing categorical accounts of automata learning. In addition, it yields new learning algorithms for several types of languages for which no such algorithms were previously known at all, including sorted languages, nominal languages with name binding, and cost functions.

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cover image ACM Conferences
LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science
July 2020
986 pages
ISBN:9781450371049
DOI:10.1145/3373718
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Published: 08 July 2020

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Author Tags

  1. Algebras
  2. Automata Learning
  3. Monads

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  • (2024)Dual Adjunction Between -Automata and Wilke Algebra QuotientsTheoretical Aspects of Computing – ICTAC 202410.1007/978-3-031-77019-7_6(96-113)Online publication date: 25-Nov-2024
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