Learning nominal automata

We present an Angluin-style algorithm to learn nominal automata, which are acceptors of languages over infinite (structured) alphabets. The abstract approach we take allows us to seamlessly extend known variations of the algorithm to this new setting. In particular we can learn a subclass of nominal non-deterministic automata. An implementation using a recently developed Haskell library for nominal computation is provided for preliminary experiments

Learning nominal automata

We present an Angluin-style algorithm to learn nominal automata, which are acceptors of languages over infinite (structured) alphabets. The abstract approach we take allows us to seamlessly extend known variations of the algorithm to this new setting. In particular we can learn a subclass of nominal non-deterministic automata. An implementation using a recently developed Haskell library for nominal computation is provided for preliminary experiments

Residual Nominal Automata

We are motivated by the following question: which nominal languages admit an active learning algorithm? This question was left open in previous work, and is particularly challenging for languages recognised by nondeterministic automata. To answer it, we develop the theory of residual nominal automata, a subclass of nondeterministic nominal automata. We prove that this class has canonical representatives, which can always be constructed via a finite number of observations. This property enables active learning algorithms, and makes up for the fact that residuality - a semantic property - is undecidable for nominal automata. Our construction for canonical residual automata is based on a machine-independent characterisation of residual languages, for which we develop new results in nominal lattice theory. Studying residuality in the context of nominal languages is a step towards a better understanding of learnability of automata with some sort of nondeterminism

Residual Nominal Automata

Nominal automata are models for accepting languages over infinite alphabets. In this paper we refine the hierarchy of nondeterministic nominal automata, by developing the theory of residual nominal automata. In particular, we show that they admit canonical minimal representatives, and that the universality problem becomes decidable. We also study exact learning of these automata, and settle questions that were left open about their learnability via observations

DEQ:Equivalence Checker for Deterministic Register Automata

Register automata are one of the most studied automata models over infinite alphabets with applications in learning, systems modelling and program verification. We present an equivalence checker for deterministic register automata, called DEQ, based on a recent polynomial-time algorithm that employs group-theoretic techniques to achieve succinct representations of the search space. We compare the performance of our tool to other available implementations, notably in the learning library RALib and nominal frameworks LOIS and NLambda

Separation and Renaming in Nominal Sets

Nominal sets provide a foundation for reasoning about names. They are used primarily in syntax with binders, but also, e.g., to model automata over infinite alphabets. In this paper, nominal sets are related to nominal renaming sets, which involve arbitrary substitutions rather than permutations, through a categorical adjunction. In particular, the left adjoint relates the separated product of nominal sets to the Cartesian product of nominal renaming sets. Based on these results, we define the new notion of separated nominal automata. We show that these automata can be exponentially smaller than classical nominal automata, if the semantics is closed under substitutions