CALF: Categorical Automata Learning Framework

Automata learning is a popular technique used to automatically construct an automaton model from queries, and much research has gone into devising specific adaptations of such algorithms for different types of automata. This thesis presents a unifying approach to many existing algorithms using category theory, which eases correctness proofs and guides the design of new automata learning algorithms. We provide a categorical automata learning framework---CALF---that at its core includes an abstract version of the popular L* algorithm. Using this abstract algorithm we derive several concrete ones. We instantiate the framework to a large class of Set functors, by which we recover for the first time a tree automata learning algorithm from an abstract framework, which moreover is the first to cover also algebras of quotiented polynomial functors. We further develop a general algorithm to learn weighted automata over a semiring. On the one hand, we identify a class of semirings, principal ideal domains, for which this algorithm terminates and for which no learning algorithm previously existed; on the other hand, we show that it does not terminate over the natural numbers. Finally, we develop an algorithm to learn automata with side-effects determined by a monad and provide several optimisations, as well as an implementation with experimental evaluation. This allows us to improve existing algorithms and opens the door to learning a wide range of automata

Coalgebraic Learning (Invited Talk)

The area of automata learning was pioneered by Angluin in the 80\u27s. Her original algorithm, which applied to regular languages and deterministic automata, has been extended to various types of automata and used in software and hardware verification. In this talk, we will take an abstract perspective at automata learning. We show how the correctness of the original algorithm and many extensions can be captured in one proof using coalgebraic techniques. We also show that a novel algorithm for nominal automata can be derived from the abstract framework