Coalgebra learning via duality

Barlocco, Simone and Kupke, Clemens and Rot, Jurriaan; Bojańczyk, Mikołaj and Simpson, Alex, eds. (2019) Coalgebra learning via duality. In: International Conference on Foundations of Software Science and Computation Structures [FoSSaCS 2019]. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) . Springer, Cham, Switzerland, pp. 62-79. ISBN 9783030171278 (

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Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as tests, based on a dual adjunction between states and logical theories. This allows us to learn, e.g., labelled transition systems, using Hennessy-Milner logic. Our main contribution is an abstract learning algorithm, together with a proof of correctness and termination.