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Université Sorbonne Paris Nord

Academic institutioneurope · fr
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Research library143linked papers
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Selected work

Representative Papers

Unifying Graded Linear Logic and Differential Operators

Feb 14, 2024International Conference on Formal Structures for Computation and Deduction

This paper addresses the challenge of unifying graded linear logic (GLL) with differential operator semantics to simultaneously capture resource sensitivity and program differentiation behavior. Methodologically, we introduce **Graded Differential Linear Logic (GDL-LC)**—the first logical system that employs the differential operator monad as a grading index for exponential modalities, thereby intrinsically aligning resource accounting with proof linearization. Our formal system is built upon constant-coefficient linear partial differential operators, distribution theory, and monadic algebra; we establish its consistency and construct the first denotational model valued in generalized functions. The results show that GDL-LC is equivalent to the graded variant of finite differential linear logic, enabling fine-grained program complexity analysis while providing the first logical foundation and semantic framework for resource-aware differential computation.

5 citations1 influentialRead paper

The Bright Side of Timed Opacity

Aug 22, 2024IEEE International Conference on Formal Engineering Methods

This paper investigates the decidability of timed opacity for Timed Automata (TAs), i.e., whether a system can conceal designated secret states from an attacker who observes timestamped actions. Methodologically, it establishes decidability boundaries across multiple restricted subclasses—including one-clock, one-action, and observable-event-recording TAs—by leveraging zone-graph construction, fixed-point computation, and language inclusion checking. Key contributions include: (i) the first fine-grained decidability map for timed opacity; (ii) the introduction of a novel “bounded-observation attacker” model, where the adversary observes only the first $N$ occurrences or $N$ timestamps of observable events, and the complete decidability characterization and algorithmic solution for opacity under this constraint; and (iii) a proof that timed opacity is decidable for all natural TA subclasses except one-action TAs and one-clock TAs with $varepsilon$-transitions, accompanied by effective decision procedures for the newly identified decidable cases.

4 citationsRead paper

What is a monoid?

Apr 16, 2025

Traditional multicategorical frameworks fail to model algebraic structures with inherently asymmetric left/right components—such as relative monads, call-by-push-value (CBPV) sequents, and categories over spans—due to their inherent symmetry. Method: We introduce and systematically develop *bi-skew multicategories*, a novel framework that intrinsically distinguishes left and right inputs, thereby enabling faithful representation of such asymmetry. Within this framework, we reconstruct monads hierarchically: left-skew multicategories capture relative monads, while bi-skew multicategories precisely model CBPV sequents and other strictly asymmetric settings. Contribution/Results: We establish a strict equivalence between monads and unbiased monads in the bi-skew setting and prove their coherence theorem. This work provides a unified, rigorous, and expressive categorical foundation for asymmetric computational semantics and generalized algebraic structures.

1 citationsRead paper
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