Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations are important. This paper exploits monads, both as a mathematical structure and a programming construct, to design and prove correct a wide class of such optimizations. Monads enable the development of a new learning algorithm and correctness proofs, building upon a general framework for automata learning based on category theory. The new algorithm is parametric on a monad, which provides a rich algebraic structure to capture non-determinism and other side-effects. We show that this allows us to uniformly capture existing algorithms, develop new ones, and add optimizations.

In this paper, we study active learning algorithms for weighted automata over a semiring. We show that a variant of Angluin's seminal L algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers.

In this paper, we study active learning algorithms for weighted automata over a semiring. We show that a variant of Angluin's seminal L ⋆ algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers.

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