Coalgebra Learning via Duality

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

Angluin learning via logic

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

Learning cover context-free grammars from structural data

We consider the problem of learning an unknown context-free grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most $\ell.$ The goal is to learn a cover context-free grammar (CCFG) with respect to $\ell$, that is, a CFG whose structural descriptions with depth at most $\ell$ agree with those of the unknown CFG. We propose an algorithm, called $LA^\ell$, that efficiently learns a CCFG using two types of queries: structural equivalence and structural membership. We show that $LA^\ell$ runs in time polynomial in the number of states of a minimal deterministic finite cover tree automaton (DCTA) with respect to $\ell$. This number is often much smaller than the number of states of a minimum deterministic finite tree automaton for the structural descriptions of the unknown grammar

Learning weighted automata over principal ideal domains

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

Learning Pomset Automata.

We extend the L⋆ algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids and automata