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Daniela Petrisan

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6 papers
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6

CSL Conference 2025 Conference Paper

Correspondences Between Codensity and Coupling-Based Liftings, a Practical Approach

  • Samuel Humeau 0002
  • Daniela Petrisan
  • Jurriaan Rot

The Kantorovich distance is a widely used metric between probability distributions. The Kantorovich-Rubinstein duality states that it can be defined in two equivalent ways: as a supremum, based on non-expansive functions into [0, 1], and as an infimum, based on probabilistic couplings. Orthogonally, there are categorical generalisations of both presentations proposed in the literature, in the form of codensity liftings and what we refer to as coupling-based liftings. Both lift endofunctors on the category Set of sets and functions to that of pseudometric spaces, and both are parameterised by modalities from coalgebraic modal logic. A generalisation of the Kantorovich-Rubinstein duality has been more nebulous - it is known not to work in some cases. In this paper we propose a compositional approach for obtaining such generalised dualities for a class of functors, which is closed under coproducts and products. Our approach is based on an explicit construction of modalities and also applies to and extends known cases such as that of the powerset functor.

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CSL Conference 2021 Conference Paper

Learning Automata and Transducers: A Categorical Approach

  • Thomas Colcombet
  • Daniela Petrisan
  • Riccardo Stabile

In this paper, we present a categorical approach to learning automata over words, in the sense of the L*-algorithm of Angluin. This yields a new generic L*-like algorithm which can be instantiated for learning deterministic automata, automata weighted over fields, as well as subsequential transducers. The generic nature of our algorithm is obtained by adopting an approach in which automata are simply functors from a particular category representing words to a "computation category". We establish that the sufficient properties for yielding the existence of minimal automata (that were disclosed in a previous paper), in combination with some additional hypotheses relative to termination, ensure the correctness of our generic algorithm.

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Highlights Conference 2020 Conference Abstract

Determinizing Probabilistic Automata via Weak Distributive Laws

  • Daniela Petrisan

In this talk we present a category-theoretic approach to obtaining a belief-state transformer, that is, a transition system where the state space carries a convex algebra structure, from a probabilistic automaton. We do so by proving the existence of a weak distributive law of the powerset monad over the distribution monad. This is joint work with Alexandre Goy.

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MFCS Conference 2017 Conference Paper

Automata in the Category of Glued Vector Spaces

  • Thomas Colcombet
  • Daniela Petrisan

In this paper we adopt a category-theoretic approach to the conception of automata classes enjoying minimization by design. The main instantiation of our construction is a new class of automata that are hybrid between deterministic automata and automata weighted over a field.

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CSL Conference 2015 Conference Paper

Leaving the Nest: Nominal Techniques for Variables with Interleaving Scopes

  • Murdoch James Gabbay
  • Dan R. Ghica
  • Daniela Petrisan

We examine the key syntactic and semantic aspects of a nominal framework allowing scopes of name bindings to be arbitrarily interleaved. Name binding (e. g. delta x. M) is handled by explicit name-creation and name-destruction brackets (e. g. <delta x M x>) which admit interleaving. We define an appropriate notion of alpha-equivalence for such a language and study the syntactic structure required for alpha-equivalence to be a congruence. We develop denotational and categorical semantics for dynamic binding and provide a generalised nominal inductive reasoning principle. We give several standard synthetic examples of working with dynamic sequences (e. g. substitution) and we sketch out some preliminary applications to game semantics and trace semantics.

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