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Automata Learning with an Incomplete Teacher

Authors Mark Moeller , Thomas Wiener, Alaia Solko-Breslin , Caleb Koch, Nate Foster , Alexandra Silva

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Author Details

Mark Moeller
  • Cornell University, Ithaca, NY, USA
Thomas Wiener
  • Cornell University, Ithaca, NY, USA
Alaia Solko-Breslin
  • University of Pennsylvania, Philadelphia, PA, USA
Caleb Koch
  • Stanford University, CA, USA
Nate Foster
  • Cornell University, Ithaca, NY, USA
Alexandra Silva
  • Cornell University, Ithaca, NY, USA


We thank Marijn Heule, Martin Leucker, and Arlindo Oliveira for their efforts in providing us access to their code and benchmarks. We also thank Akshat Singh and Sheetal Athrey, with whom this project began as an undergraduate research project.

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Mark Moeller, Thomas Wiener, Alaia Solko-Breslin, Caleb Koch, Nate Foster, and Alexandra Silva. Automata Learning with an Incomplete Teacher. In 37th European Conference on Object-Oriented Programming (ECOOP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 263, pp. 21:1-21:30, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


The preceding decade has seen significant interest in use of active learning to build models of programs and protocols. But existing algorithms assume the existence of an idealized oracle - a so-called Minimally Adequate Teacher (MAT) - that cannot be fully realized in practice and so is usually approximated with testing. This work proposes a new framework for active learning based on an incomplete teacher. This new formulation, called iMAT, neatly handles scenarios in which the teacher has access to only a finite number of tests or otherwise has gaps in its knowledge. We adapt Angluin’s L^⋆ algorithm for learning finite automata to incomplete teachers and we build a prototype implementation in OCaml that uses an SMT solver to help fill in information not supplied by the teacher. We demonstrate the behavior of our iMAT prototype on a variety of learning problems from a standard benchmark suite.

Subject Classification

ACM Subject Classification
  • Theory of computation → Active learning
  • Finite Automata
  • Active Learning
  • SMT Solvers


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