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.

Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations are important. This paper exploits monads, both as a mathematical structure and a programming construct, to design and prove correct a wide class of such optimizations. Monads enable the development of a new learning algorithm and correctness proofs, building upon a general framework for automata learning based on category theory. The new algorithm is parametric on a monad, which provides a rich algebraic structure to capture non-determinism and other side-effects. We show that this allows us to uniformly capture existing algorithms, develop new ones, and add optimizations.

In this paper we recast the classical Darondeau–Degano’s causal semantics of concurrency in a coalgebraic setting, where we derive a compact model. Our construction is inspired by the one of Montanari and Pistore yielding causal automata, but we show that it is instance of an existing categorical framework for modeling the semantics of nominal calculi, whose relevance is further demonstrated. The key idea is to represent events as names, and\ud the occurrence of a new event as name generation. We model causal semantics as a coalgebra\ud over a presheaf, along the lines of the Fiore–Turi approach to the semantics of nominal\ud calculi. More specifically, we take a suitable category of finite posets, representing causal\ud relations over events, and we equip it with an endofunctor that allocates new events and\ud relates them to their causes. Presheaves over this category express the relationship between\ud processes and causal relations among the processes’ events. We use the allocation operator to\ud define a category of well-behaved coalgebras: it models the occurrence of a new event along\ud each transition. Then we turn the causal transition relation into a coalgebra in this category,\ud where labels only exhibit maximal events with respect to the source states’ poset, and we\ud show that its bisimilarity is essentially Darondeau–Degano’s strong causal bisimilarity. This\ud coalgebra is still infinite-state, but we exploit the equivalence between coalgebras over a\ud class of presheaves and History Dependent automata to derive a compact representation,\ud where states only retain the poset of the most recent events for each atomic subprocess, and\ud are isomorphic up to order-preserving permutations. Remarkably, this reduction of states is\ud automatically performed along the equivalence

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