Coalgebra Learning via Duality

Barlocco, Simone; Kupke, Clemens; Rot, Jurriaan

doi:10.1007/978-3-030-17127-8_4

Cited by 18 publications

(27 citation statements)

References 26 publications

(33 reference statements)

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“…Instantiation of the abstract algorithm to concrete categories and functors (Section 6), providing the first learning algorithm for tree automata derived abstractly. The work in the present paper complements other recent work on abstract automata learning algorithms: Barlocco, Kupke, and Rot [12] gave an algorithm for coalgebras of a functor, whereas Urbat and Schröder [26] provided an algorithm for structures that can be represented as both algebras and coalgebras. Our focus instead is on algebras, such as tree automata, that cannot be covered by the aforementioned frameworks.…”

Section: Introductionsupporting

confidence: 56%

“…Barlocco et al [12] proposed an abstract algorithm for learning coalgebras. It stipulates the tests to be formed by an abstract version of coalgebraic modal logic.…”

Section: Related Workmentioning

confidence: 99%

“…It stipulates the tests to be formed by an abstract version of coalgebraic modal logic. On the one hand, the notion of wrapper and closedness from CALF essentially instantiate to that setting; on the other hand, the combination of logic and coalgebra is precisely what enables to define an actual learning algorithm in [12]. The current work focus on algebras rather than coalgebras, and is orthogonal.…”

Section: Related Workmentioning

confidence: 99%

“…The current work focus on algebras rather than coalgebras, and is orthogonal. In particular, it covers (bottom-up) tree automata, which is outside the scope of [12].…”

Section: Related Workmentioning

confidence: 99%

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A Categorical Framework for Learning Generalised Tree Automata

Heerdt¹,

Kappé²,

Rot³

et al. 2020

Preprint

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Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify these using category theory in order to ease correctness proofs and guide the design of new algorithms. In this paper, we extend CALF to cover learning of algebraic structures that may not have a coalgebraic presentation. Furthermore, we provide a detailed algorithmic account of an abstract version of the popular L ⋆ algorithm, which was missing from CALF. We instantiate the abstract theory to a large class of Set functors, by which we recover for the first time practical tree automata learning algorithms from an abstract framework and at the same time obtain new algorithms to learn algebras of quotiented polynomial functors.

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Section: Introductionsupporting

confidence: 56%

“…Barlocco et al [12] proposed an abstract algorithm for learning coalgebras. It stipulates the tests to be formed by an abstract version of coalgebraic modal logic.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…The current work focus on algebras rather than coalgebras, and is orthogonal. In particular, it covers (bottom-up) tree automata, which is outside the scope of [12].…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

A Categorical Framework for Learning Generalised Tree Automata

Heerdt¹,

Kappé²,

Rot³

et al. 2020

Preprint

Self Cite

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“…Consider for instance automata theory: deterministic automata can be conveniently regarded as certain kind of coalgebras on Set [33], nondeterministic automata as the same kind of coalgebras but on EM(P f ) [35], and weighted automata on EM(S) [4]. Here, P f is the finite powerset monad, modelling nondeterministic computations, while S is the monad of semimodules over a semiring S, modelling various sorts of quantitative aspects when varying the underlying semiring S. It is worth mentioning two facts: first, rather than taking coalgebras over EM(T ), the category of algebras for the monad T , one can also consider coalgebras over Kl(T ), the Kleisli category induced by T [20]; second, these two approaches based on monads have lead not only to a deeper understanding of the subject, but also to effective proof techniques [6,7,14], algorithms [1,8,22,36,39] and logics [19,21,27].…”

Section: Introductionmentioning

confidence: 99%

Combining Semilattices and Semimodules

Bonchi

Santamaria

2021

Lecture Notes in Computer Science

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We describe the canonical weak distributive law $$\delta :\mathcal S\mathcal P\rightarrow \mathcal P\mathcal S$$ δ : S P → P S of the powerset monad $$\mathcal P$$ P over the S-left-semimodule monad $$\mathcal S$$ S , for a class of semirings S. We show that the composition of $$\mathcal P$$ P with $$\mathcal S$$ S by means of such $$\delta $$ δ yields almost the monad of convex subsets previously introduced by Jacobs: the only difference consists in the absence in Jacobs’s monad of the empty convex set. We provide a handy characterisation of the canonical weak lifting of $$\mathcal P$$ P to $$\mathbb {EM}(\mathcal S)$$ EM ( S ) as well as an algebraic theory for the resulting composed monad. Finally, we restrict the composed monad to finitely generated convex subsets and we show that it is presented by an algebraic theory combining semimodules and semilattices with bottom, which are the algebras for the finite powerset monad $$\mathcal P_f$$ P f .

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A New Approach for Active Automata Learning Based on Apartness

Vaandrager

Garhewal

Rot

et al. 2022

Lecture Notes in Computer Science

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We present $$L^{\#}$$ L # , a new and simple approach to active automata learning. Instead of focusing on equivalence of observations, like the $$L^{*}$$ L ∗ algorithm and its descendants, $$L^{\#}$$ L # takes a different perspective: it tries to establish apartness, a constructive form of inequality. $$L^{\#}$$ L # does not require auxiliary notions such as observation tables or discrimination trees, but operates directly on tree-shaped automata. $$L^{\#}$$ L # has the same asymptotic query and symbol complexities as the best existing learning algorithms, but we show that adaptive distinguishing sequences can be naturally integrated to boost the performance of $$L^{\#}$$ L # in practice. Experiments with a prototype implementation, written in Rust, suggest that $$L^{\#}$$ L # is competitive with existing algorithms.

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Coalgebra Learning via Duality

Cited by 18 publications

References 26 publications

A Categorical Framework for Learning Generalised Tree Automata

A Categorical Framework for Learning Generalised Tree Automata

Combining Semilattices and Semimodules

A New Approach for Active Automata Learning Based on Apartness

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