Learning Pomset Automata

Guarded Kleene Algebra with Tests: Automata Learning

“…More recently, there have been efforts to give a unifying perspective on those approaches. In this thesis, we present a categorytheoretic framework that generalises ideas of Van Heerdt [63,64,66], the notion of a scoop by Arbib and Manes [19], and the universal-algebraic treatment of Myers et al [119]. We present the first general algorithm for the construction of succinct automata and give a unifying minimality result.…”

“…Their construction, however, is restricted to nondeterministic automata, and does not provide a general algorithm to construct a succinct automaton. A different unifying perspective was given by van Heerdt [66,63,64]. One of the central notions in van Heerdt's work is the concept of a scoop, originally introduced by Arbib and Manes [19], and essentially a simple categorytheoretic generalisation of algebraic generators.…”

“…For example, for the above functor F with F X = 2 × X A , the final coalgebra is carried by the set of all languages A * → 2, and the final coalgebra homomorphism assigns to a state x of an unpointed deterministic automaton the language it accepts, when given the initial state x. This simplicity has lead to, among others, coalgebra successfully serving as a framework for the generalisation of automata learning algorithms in the style of L * [80,63,64].…”

“…A more general and unifying perspective on learning automata that may not have a canonical target was given by Van Heerdt [66,63,64]. One of the central notions in this work is the concept of a scoop, originally introduced by Arbib and Manes [19] and here referred to as a generator.…”

“…A * → Ω, that is, M L = m im(obs) . In more detail: Ω is carried by B A * ; obs satisfies obs(w)(v) = L(wv); and A * is equipped with the F -coalgebra structure ε, δ : A * → B × (A * ) A defined by ε(w) = L(w) and δ(w)(a) = wa [63].…”