Angluin learning via logic

Barlocco, Simone and Kupke, Clemens; Artemov, Sergei and Nerode, Anil, eds. (2017) Angluin learning via logic. In: Logical Foundations of Computer Science. Lecture Notes in Computer Science . Springer, USA, pp. 72-90. ISBN 9783319720555

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Abstract

In this paper we will provide a fresh take on Dana Angluin's algorithm for learning using ideas from coalgebraic modal logic. Our work opens up possibilities for applications of tools & techniques from modal logic to automata learning and vice versa. As main technical result we obtain a generalisation of Angluin's original algorithm from DFAs to coalgebras for an arbitrary finitary set functor T in the following sense: given a (possibly infinite) pointed T-coalgebra that we assume to be regular (i.e. having an equivalent finite representation) we can learn its finite representation by asking (i) "logical queries" (corresponding to membership queries) and (ii) making conjectures to which the teacher has to reply with a counterexample. This covers (a known variant) of the original L* algorithm and the learning of Mealy/Moore machines. Other examples are bisimulation quotients of (probabilistic) transition systems.