Angluin Learning via Logic

Abstract

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.

Coalgebra Learning via Duality

“…Related work. The idea that tests in the learning algorithm should be formulas of a distinct logical language was proposed first in [6]. However, the work in loc.cit.…”

“…This paper is a significant improvement: the dual adjunction framework and the definition of the base [8] enables us to present a description of Angluin's algorithm in purely categorical terms, including a proof of correctness and, crucially, termination. Our abstract notion of logic also enables us to recover exactly the standard DFA algorithm (where tests are words) and the algorithm for learning Mealy machines (where test are many-valued), something that is not possible in [6] where tests are modal formulas. Closely related to our work is also the line of research initiated by [16] and followed up within the CALF project [12,13,14] which applies ideas from category theory to automata learning.…”

Learning Pomset Automata

“…Note that the algorithm does not explicitly check for consistency; this is because we actually ensure a stronger property-sharpness [3]-as an invariant (Lemma 25). This property ensures every row indexed by a pomset in S is indexed by exactly one pomset in S (implying consistency):…”

Survey on Learning-Based Formal Methods: Taxonomy, Applications and Possible Future Directions

“…They presented the first step towards a categorical understanding and generalization of Angluin's learning algorithm, originally defined for DFA. In [132], Barlocco and Kupke provided a fresh take on Dana Angluin's algorithm for learning using ideas from coalgebraic modal logic, and proposed the "L co algorithm", which is a generalization of Angluin's original algorithm from DFAs to coalgebras. It allows the learning of regular coalgebras for an arbitrary finitary set functor.…”