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   {"id":"aristoteLearningWeightedAutomata2025a","abstract":"We study automata weighted over number rings, that is, rings of integers in an algebraic number field.\n\nWe show that number rings are what we call \"almost strong Fatou\": if an n-state automaton weighted in a number field recognizes an integer-valued series, then it admits an equivalent n+1-state automaton weighted in the corresponding ring of integers.\n\nWe give a polynomial-time algorithm for computing such an n+1-state automaton, and show that removing any more states is at least as hard as solving the principal ideal problem, for which the best currently known algorithm is in quantum polynomial time.\n\nFinally, we will see how this procedure can be used to reduce active learning problems in number rings to active learning problems in fields. If time allows, I will also give a brief explanation of how this generalizes to a generic reduction procedure between active learning problems for automata valued in different categories.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteLearningWeightedAutomata2025a","event-place":"Marseille, France","event-title":"MoVe seminar (LiS)","genre":"seminar","issued":{"date-parts":[["2025",3,28]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/8b14ed9a7383f9776fc69aa03003890a/dedekind-weighted-automata.pdf","publisher-place":"Marseille, France","title":"Learning weighted automata over number rings, concretely (and categorically)","type":"speech","URL":"https://move.lis-lab.fr/seminars"},
   {"id":"aristoteLearningWeightedAutomata2025b","abstract":"We develop a generic reduction procedure for active learning problems. Our approach is inspired by a recent polynomial-time reduction of the exact learning problem for weighted automata over integers to that for weighted automata over rationals (Buna-Marginean et al. 2024). Our procedure improves the efficiency of a category-theoretic automata learning algorithm, and poses new questions about the complexity of its implementation when instantiated to concrete categories. \n\nAs our second main contribution, we address these complexity aspects in the concrete setting of learning weighted automata over number rings, that is, rings of integers in an algebraic number field. Assuming a full representation of a number ring OK, we obtain an exact learning algorithm of OK-weighted automata that runs in polynomial time in the size of the target automaton, the logarithm of the length of the longest counterexample, the degree of the number field, and the logarithm of its discriminant. Our algorithm produces an automaton that has at most one more state than the minimal one, and we prove that doing better requires solving the principal ideal problem, for which the best currently known algorithm is in quantum polynomial time.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteLearningWeightedAutomata2025b","event-place":"Wadern, Germany","event-title":"Dagstuhl Seminar 25141: Categories for Automata and Language Theory","genre":"conference","issued":{"date-parts":[["2025",3,31]]},"language":"en","note":"slides: https://materials.dagstuhl.de/index.php?semnr=25141&fileId=17258","publisher-place":"Wadern, Germany","title":"Learning weighted automata over number rings, (concretely and) categorically","type":"speech","URL":"https://www.dagstuhl.de/25141"},
   {"id":"aristoteLearningWeightedAutomata2025c","abstract":"We develop a generic reduction procedure for active learning problems. Our approach is inspired by a recent polynomial-time reduction of the exact learning problem for weighted automata over integers to that for weighted automata over rationals (Buna-Marginean et al. 2024). Our procedure improves the efficiency of a category-theoretic automata learning algorithm, and poses new questions about the complexity of its implementation when instantiated to concrete categories.\n\nAs our second main contribution, we address these complexity aspects in the concrete setting of learning weighted automata over number rings, that is, rings of integers in an algebraic number field. Assuming a full representation of a number ring OK, we obtain an exact learning algorithm of OK-weighted automata that runs in polynomial time in the size of the target automaton, the logarithm of the length of the longest counterexample, the degree of the number field, and the logarithm of its discriminant. Our algorithm produces an automaton that has at most one more state than the minimal one, and we prove that doing better requires solving the principal ideal problem, for which the best currently known algorithm is in quantum polynomial time.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteLearningWeightedAutomata2025c","event-place":"Singapore, Singapore","event-title":"Fortieth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2025)","genre":"conference","issued":{"date-parts":[["2025",6,24]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/13561d884f911e1e27f5df625892bfb1/dedekind-weighted-automata.pdf","publisher-place":"Singapore, Singapore","title":"Learning weighted automata over number rings, concretely and categorically","type":"speech","URL":"https://lics.siglog.org/lics25/"},
+  {"id":"aristoteLearningWeightedAutomata2025d","abstract":"We study automata weighted over number rings, that is, rings of integers in an algebraic number field.\n\nWe show that number rings are what we call “almost strong Fatou”: if an n-state automaton weighted in a number field recognizes an integer-valued series, then it admits an equivalent n+1-state automaton weighted in the corresponding ring of integers.\n\nWe give a polynomial-time algorithm for computing such an n+1-state automaton, and show that removing any more states is at least as hard as solving the principal ideal problem, for which the best currently known algorithm is in quantum polynomial time.\n\nFinally, we will see how this procedure can be used to reduce active learning problems in number rings to active learning problems in fields. If time allows, I will also give a brief teaser of how this generalizes to a generic reduction procedure between active learning problems for automata valued in different categories. These categorical aspects will be further developed on May 15th for a talk at the AutCat seminar.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteLearningWeightedAutomata2025d","event-place":"Paris, France","event-title":"Séminaire Automates (IRIF)","genre":"seminar","issued":{"date-parts":[["2025",5,9]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/8b14ed9a7383f9776fc69aa03003890a/dedekind-weighted-automata.pdf","publisher-place":"Paris, France","title":"Learning weighted automata over number rings, concretely (and categorically)","type":"speech","URL":"https://www.irif.fr/seminaires/automates/index"},
+  {"id":"aristoteLearningWeightedAutomata2025e","abstract":"We study automata weighted over number rings, that is rings of integers in an algebraic number field. Assuming a full representation of a number ring O_K, we obtain an exact learning algorithm of O_K-weighted automata that runs in polynomial time in the size of the target automaton, the logarithm of the length of the longest counterexample, the degree of the number field, and the logarithm of its discriminant. Our algorithm produces an automaton that has at most one more state than the minimal one, and we prove that doing better requires solving the principal ideal problem, for which the best currently known algorithm is in quantum polynomial time.\n\nMore generally, we develop a generic reduction procedure for active learning problems. Our approach is inspired by a recent polynomial-time reduction of the exact learning problem for weighted automata over integers to that for weighted automata over rationals (Buna-Marginean et al. 2024), and improves the efficiency of a category-theoretic automata learning algorithm.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteLearningWeightedAutomata2025e","event-place":"Marne-la-Vallée, France","event-title":"Annual Meeting ot the GT Data, Automata, Algebra & Logic (DAAL)","genre":"conference","issued":{"date-parts":[["2025",5,13]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/9417c336e556b40905375981c1baee1b/dedekind-weighted-automata.pdf","publisher-place":"Marne-la-Vallée, France","title":"Learning weighted automata over number rings, concretely and categorically","type":"speech","URL":"https://www-igm.univ-mlv.fr/~marsault/daal2025/"},
   {"id":"aristoteMonotoneWeakDistributive2024a","abstract":"Noticing the similarity between the monotone weak distributive laws combining two layers of nondeterminisms in sets and in compact Hausdorff spaces, we study whether the latter law can be obtained automatically as a weak lifting of the former. This holds partially, but does not generalize to other categories of algebras: we then characterize when exactly monotone weak distributive laws over powerset monads in categories of algebras exist, exhibiting a law combining probabilities and non-determinism in compact Hausdorff spaces and showing on the other hand that such laws do not exist in a lot of other cases.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMonotoneWeakDistributive2024a","event-place":"Leiden, Netherlands","event-title":"109th Peripatetic Seminar on Sheaves and Logic (PSSL 109)","genre":"conference","issued":{"date-parts":[["2024",11,15]]},"language":"en","note":"slides: https://dutchcats.github.io/PSSL-2024/slides_PSSL24/Aristote-PSSL109.pdf","publisher-place":"Leiden, Netherlands","title":"Monotone weak distributive laws over the lifted powerset monad in categories of algebras","type":"speech","URL":"https://dutchcats.github.io/PSSL-2024/"},
   {"id":"aristoteMonotoneWeakDistributive2025a","abstract":"In both the category of sets and the category of compact Hausdorff spaces, there is a monotone weak distributive law that combines two layers of non-determinism. Noticing the similarity between these two laws, we study whether the latter can be obtained automatically as a weak lifting of the former. This holds partially, but does not generalize to other categories of algebras. We then characterize when exactly monotone weak distributive laws over powerset monads in categories of algebras exist, on the one hand exhibiting a law combining probabilities and non-determinism in compact Hausdorff spaces and showing on the other hand that such laws do not exist in a lot of other cases.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMonotoneWeakDistributive2025a","event-place":"Jena, Germany","event-title":"42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)","genre":"conference","issued":{"date-parts":[["2025",3,5]]},"language":"en","note":"slides: https://stacs2025.gitlab.io/slides/monotone-weak-distributive-laws-over-the-lifted-powerset-monad-in-categories-of-algebras.pdf","publisher-place":"Jena, Germany","title":"Monotone weak distributive laws over the lifted powerset monad in categories of algebras","type":"speech","URL":"https://stacs2025.de/"},
   {"id":"aristoteMonotoneWeakDistributive2025b","abstract":"Within the study of the semantics of programming languages, computational effects may be modelled with monads, and weak distributive laws between monads are then a tool to combine two such effects.\n\nIn both the category of sets and the category of compact Hausdorff spaces, there is a monotone weak distributive law that combines two layers of non-determinism. Noticing the similarity between these two laws, we study whether the latter can be obtained automatically as some sort of lifting of the former.\n\nMore specifically, we show how a framework for constructing monotone weak distributive laws in regular categories lifts to categories of algebras, giving a full characterization for the existence of monotone weak distributive laws therein. We then exhibit such a law, combining probabilities and non-determinism, in compact Hausdorff spaces; but we also show how such laws do not exist in a lot of other cases.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMonotoneWeakDistributive2025b","event-place":"Marseille, France","event-title":"LSC Seminar (LiS)","genre":"seminar","issued":{"date-parts":[["2025",3,27]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1062/uploads/02cd7ed45cdac419f5cf315fdde2200a/monotone-wdl-algebras.pdf","publisher-place":"Marseille, France","title":"Monotone weak distributive laws over the lifted powerset monad in categories of algebras","type":"speech","URL":"https://lsc.lis-lab.fr/lsc-seminar/"},