26 Search Results for "Cohen, Cyril"

Document
DOI: 10.4230/LIPIcs.CSL.2026.18
A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light

Authors: Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We extend the existing HOL Light Library for Modal Systems (HOLMS) to support a modular implementation of modal reasoning within the HOL Light proof assistant. We deeply embed axiomatic calculi and relational semantics for seven normal modal logics (K, T, B, K4, S4, S5, GL) and formalise modal adequacy theorems for these systems. We then leverage those formalisations to implement a mechanism for automated reasoning via proof-search in the associated labelled sequent calculi, which we shallowly embed in HOL Light’s goal-stack mechanism. This way, we equip the general-purpose proof assistant with (semi)decision procedures for these logics that, in case of failure to construct a proof for the input formula, return a certified countermodel within the appropriate class for the logic under consideration. On the methodological side, we propose a precise measure of the modularity of our approach by systematically adopting Christopher Strachey’s distinction between ad hoc and parametric polymorphism throughout the library.
Cite as

Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi. A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 18:1-18:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bilotta_et_al:LIPIcs.CSL.2026.18,
  author =	{Bilotta, Antonella and Maggesi, Marco and Perini Brogi, Cosimo},
  title =	{{A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{18:1--18:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.18},
  URN =		{urn:nbn:de:0030-drops-254427},
  doi =		{10.4230/LIPIcs.CSL.2026.18},
  annote =	{Keywords: Modal logic, HOL Light, Labelled sequent calculi, Logical verification, Interactive theorem proving, Automated proof-search}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.31
Delaunay Triangulations with Predictions

Authors: Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set P of n points in the plane and a triangulation G that serves as a "prediction" of the Delaunay triangulation, we would like to use G to compute the correct Delaunay triangulation DT(P) more quickly when G is "close" to DT(P). We obtain a variety of results of this type, under different deterministic and probabilistic settings, including the following: 1) Define D to be the number of edges in G that are not in DT(P). We present a deterministic algorithm to compute DT(P) from G in O(n + Dlog³ n) time, and a randomized algorithm in O(n+Dlog n) expected time, the latter of which is optimal in terms of D. 2) Let R be a random subset of the edges of DT(P), where each edge is chosen independently with probability ρ. Suppose G is any triangulation of P that contains R. We present an algorithm to compute DT(P) from G in O(nlog log n + nlog(1/ρ)) time with high probability. 3) Define d_{vio} to be the maximum number of points of P strictly inside the circumcircle of a triangle in G (the number is 0 if G is equal to DT(P)). We present a deterministic algorithm to compute DT(P) from G in O(nlog^*n + nlog d_{vio}) time. We also obtain results in similar settings for related problems such as 2D Euclidean minimum spanning trees, and hope that our work will open up a fruitful line of future research.
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Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos. Delaunay Triangulations with Predictions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cabello_et_al:LIPIcs.ITCS.2026.31,
  author =	{Cabello, Sergio and Chan, Timothy M. and Giannopoulos, Panos},
  title =	{{Delaunay Triangulations with Predictions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{31:1--31:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.31},
  URN =		{urn:nbn:de:0030-drops-253186},
  doi =		{10.4230/LIPIcs.ITCS.2026.31},
  annote =	{Keywords: Delaunay Triangulation, Minimum Spanning Tree, Algorithms with Predictions}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.43
New Approximate Distance Oracles and Their Applications

Authors: Avi Kadria and Liam Roditty

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Let G = (V, E) be an undirected graph with n vertices and m edges, and let μ = m/n. A distance oracle is a data structure designed to answer approximate distance queries, with the goal of achieving low stretch, efficient space usage, and fast query time. While much of the prior work focused on distance oracles with constant query time, this paper presents a comprehensive study of distance oracles with non-constant query time. We explore the tradeoffs between space, stretch, and query time of distance oracles in various regimes. Specifically, we consider both weighted and unweighted graphs in the regimes of stretch < 2 and stretch ≥ 2. In addition, we demonstrate several applications of our new distance oracles to the n-Pairs Shortest Paths (n-PSP) problem and the All Nodes Shortest Cycles (ANSC) problem. Our main contributions are: - Weighted graphs: We present a new three-way trade-off between stretch, space, and query time, offering a natural extension of the classical Thorup–Zwick distance oracle [STOC’01 and JACM’05] to regimes with larger query time. Specifically, for any 0 < r < 1/2 and integer k ≥ 1, we construct a (2k(1 - 2r) - 1)-stretch distance oracle with Õ(m + n^{1 + 1/k}) space and Õ(μ n^r) query time. This construction provides an asymptotic improvement over the classical (2k - 1)-stretch and O(n^{1 + 1/k})-space tradeoff of Thorup and Zwick in sparse graphs, at the cost of increased query time. We also improve upon a result of Dalirrooyfard et al. [FOCS’22], who presented a (2k - 2)-stretch distance oracle with O(m + n^{1 + 1/k}) space and O(μ n^{1/k}) query time. In our oracle we reduce the stretch from (2k - 2) to (2k - 5) while preserving the same space and query time. - Unweighted graphs: We present a (2k - 5, 4 + 2_{odd})-approximation distance oracle with O(n^{1 + 1/k}) space and O(n^{1/k}) query time. This improves upon a (2k - 2, 2_{odd})-approximation distance oracle of Dalirrooyfard et al. [FOCS’22] while maintaining the same space and query time. We also present a distance oracle that given u,v ∈ V returns an estimate d̂(u,v) ≤ d(u,v) + 2⌈ d(u,v) / 3 ⌉ + 2, using O(n^{4/3 + 2ε}) space and O(n^{1 - 3ε}) query time. To the best of our knowledge, this is the first distance oracle that simultaneously achieves a multiplicative stretch < 2, and a space complexity O(n^{1.5 - α}), for some α > 0. - Applications for n-PSP and ANSC: We present an Õ(m^{1 - 1/(k+1)} n)-time algorithm for the n-PSP problem, that for every input pair ⟨s_i,t_i⟩, where i ∈ [n], returns an estimate d̂(s_i, t_i) such that d̂(s_i,t_i) ≤ d(s_i,t_i) + 2⌈d(s_i,t_i)/2k⌉. By allowing a small additive error, this result circumvents the conditional running time lower bound of Ω(m^{2 - 2/(k+1)} ⋅ n^{1/(k+1) - o(1)}), established by Dalirrooyfard et al. [FOCS’22] for achieving (1 + 1/k)-stretch. Additionally, we present an Õ(mn^{1 - 1/k})-time algorithm for the ANSC problem that computes, for every u ∈ V, an estimate ĉ_u such that ĉ_u ≤ SC(u) + 2⌈SC(u)/2(k - 1)⌉, where SC(u) denotes the length of the shortest cycle containing u. This improves upon the Õ(m^{2 - 2/k}n^{1/k})-time algorithm of Dalirrooyfard et al. [FOCS'22], while achieving the same approximation guarantee. We obtain our results by developing several new techniques, among them are the borderline vertices technique and the middle vertex technique, which may be of independent interest.
Cite as

Avi Kadria and Liam Roditty. New Approximate Distance Oracles and Their Applications. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kadria_et_al:LIPIcs.ISAAC.2025.43,
  author =	{Kadria, Avi and Roditty, Liam},
  title =	{{New Approximate Distance Oracles and Their Applications}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{43:1--43:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.43},
  URN =		{urn:nbn:de:0030-drops-249514},
  doi =		{10.4230/LIPIcs.ISAAC.2025.43},
  annote =	{Keywords: Distance oracles, Fine-grained algorithms, Graph algorithms, Data structures}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.17
Deterministic Synchronous Self-Stabilizing BFS Construction with Constant Space Complexity

Authors: Lélia Blin, Franck Petit, and Sébastien Tixeuil

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
In this paper, we resolve a long-standing open problem in self-stabilization asking whether it is possible to construct a spanning tree using constant memory per node in a synchronous semi-uniform networks, i.e., networks in which one node is distinguished. We design a synchronous self-stabilizing algorithm that constructs a breadth-first search (BFS) tree in any anonymous semi-uniform network using only a constant number of bits of memory per node. Crucially, our approach operates without any prior knowledge of global network parameters such as maximum degree, diameter, or number of nodes. In contrast to traditional self-stabilizing methods - such as pointer-to-neighbors, distance-to-root, or identifiers - that are unsuitable under strict memory constraints, our solution employs an innovative constant-space token dissemination mechanism. This mechanism effectively eliminates cycles and rectifies errors in the BFS structure, ensuring both correctness and memory efficiency. The proposed algorithm not only meets the stringent requirements of memory-constrained distributed systems, but also opens new avenues for research in the design of self-stabilizing protocols under severe resource limitations: constant space-complexity may not systematically prevent the existence of self-stabilizing algorithms for important non-trivial tasks.
Cite as

Lélia Blin, Franck Petit, and Sébastien Tixeuil. Deterministic Synchronous Self-Stabilizing BFS Construction with Constant Space Complexity. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blin_et_al:LIPIcs.DISC.2025.17,
  author =	{Blin, L\'{e}lia and Petit, Franck and Tixeuil, S\'{e}bastien},
  title =	{{Deterministic Synchronous Self-Stabilizing BFS Construction with Constant Space Complexity}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.17},
  URN =		{urn:nbn:de:0030-drops-248349},
  doi =		{10.4230/LIPIcs.DISC.2025.17},
  annote =	{Keywords: Distributed algorithms, fault-tolerance, transient faults, self-stabilization, memory optimization}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.20
Selfish Mining Under General Stochastic Rewards

Authors: Maryam Bahrani, Michael Neuder, and S. Matthew Weinberg

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
Selfish miners selectively withhold blocks to earn disproportionately high revenue. The vast majority of the selfish mining literature focuses exclusively on block rewards. [Carlsten et al., 2016] is a notable exception, observing that similar strategic behavior is profitable in a zero-block-reward regime (the endgame for Bitcoin’s quadrennial halving schedule) if miners are compensated with transaction fees alone. Neither model fully captures miner incentives today. The block reward remains 3.125 BTC, yet some blocks yield significantly higher revenue. For example, congestion during the launch of the Babylon protocol in August 2024 caused transaction fees to spike from 0.14 BTC to 9.52 BTC, a 68× increase in fees within two blocks. Our results are both practical and theoretical. Of practical interest, we study selfish mining profitability under a combined reward function that more accurately models miner incentives. This analysis enables us to make quantitative claims about protocol risk (e.g., the mining power at which a selfish strategy becomes profitable is reduced by 22% when optimizing over the combined reward function versus block rewards alone) and qualitative observations (e.g., a miner considering both block rewards and transaction fees will mine more or less aggressively respectively than if they cared about either alone). These practical results follow from our novel model and methodology, which constitute our theoretical contributions. We model general, time-accruing stochastic rewards in the Nakamoto Consensus Game, which requires explicit treatment of difficult adjustment and randomness; we characterize reward function structure through a set of properties (e.g., that rewards accrue only as a function of time since the parent block). We present a new methodology to analytically calculate expected selfish miner rewards under a broad class of stochastic reward functions and validate our method numerically by comparing it with the existing literature and simulating the combined reward sources directly.
Cite as

Maryam Bahrani, Michael Neuder, and S. Matthew Weinberg. Selfish Mining Under General Stochastic Rewards. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bahrani_et_al:LIPIcs.AFT.2025.20,
  author =	{Bahrani, Maryam and Neuder, Michael and Weinberg, S. Matthew},
  title =	{{Selfish Mining Under General Stochastic Rewards}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{20:1--20:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.20},
  URN =		{urn:nbn:de:0030-drops-247396},
  doi =		{10.4230/LIPIcs.AFT.2025.20},
  annote =	{Keywords: Proof-of-Work, Selfish Mining, MEV}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.39
Going Beyond Surfaces in Diameter Approximation

Authors: Michał Włodarczyk

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge weights, there are known (1+ε)-approximation algorithms with running time poly(1/ε, log n)⋅ n. However, these algorithms rely on shortest path separators and this technique falls short to yield efficient algorithms beyond graphs of bounded genus. In this work we depart from embedding-based arguments and obtain diameter approximations relying on VC set systems and the local treewidth property. We present two orthogonal extensions of the planar case by giving (1+ε)-approximation algorithms with the following running times: - 𝒪_h((1/ε)^𝒪(h) ⋅ nlog² n)-time algorithm for graphs excluding an apex graph of size h as a minor, - 𝒪_d((1/ε)^𝒪(d) ⋅ nlog² n)-time algorithm for the class of d-apex graphs. As a stepping stone, we obtain efficient (1+ε)-approximate distance oracles for graphs excluding an apex graph of size h as a minor. Our oracle has preprocessing time 𝒪_h((1/ε)⁸⋅ nlog nlog W) and query time 𝒪_h((1/ε)²⋅log n log W), where W is the metric stretch. Such oracles have been so far only known for bounded genus graphs. All our algorithms are deterministic.
Cite as

Michał Włodarczyk. Going Beyond Surfaces in Diameter Approximation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.ESA.2025.39,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Going Beyond Surfaces in Diameter Approximation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{39:1--39:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.39},
  URN =		{urn:nbn:de:0030-drops-245076},
  doi =		{10.4230/LIPIcs.ESA.2025.39},
  annote =	{Keywords: diameter, approximation, distance oracles, graph minors, treewidth}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.21
Formalizing Concentration Inequalities in Rocq: Infrastructure and Automation

Authors: Reynald Affeldt, Alessandro Bruni, Cyril Cohen, Pierre Roux, and Takafumi Saikawa

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Concentration inequalities are standard lemmas providing upper bounds on deviations of random variables. To formalize concentration inequalities, we have been developing a general library of lemmas for probability theory in the Rocq prover. This effort led us to revisit already established technical aspects of the Mathematical Components libraries. In this paper, we report on improvements of general interest resulting from our formalization. We devise types for numeric values and a lightweight semi-decision procedure, based on interval arithmetic. We also extend the hierarchy of available mathematical structures to formalize Lebesgue spaces. We illustrate our new formalization of probability theory with the complete proof of a concentration inequality for Bernoulli sampling.
Cite as

Reynald Affeldt, Alessandro Bruni, Cyril Cohen, Pierre Roux, and Takafumi Saikawa. Formalizing Concentration Inequalities in Rocq: Infrastructure and Automation. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{affeldt_et_al:LIPIcs.ITP.2025.21,
  author =	{Affeldt, Reynald and Bruni, Alessandro and Cohen, Cyril and Roux, Pierre and Saikawa, Takafumi},
  title =	{{Formalizing Concentration Inequalities in Rocq: Infrastructure and Automation}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.21},
  URN =		{urn:nbn:de:0030-drops-246195},
  doi =		{10.4230/LIPIcs.ITP.2025.21},
  annote =	{Keywords: Rocq prover, Mathematical Components library, abstraction interpretation, probability theory, concentration inequalities}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.1
A Certified Proof Checker for Deep Neural Network Verification in Imandra

Authors: Remi Desmartin, Omri Isac, Grant Passmore, Ekaterina Komendantskaya, Kathrin Stark, and Guy Katz

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Recent advances in the verification of deep neural networks (DNNs) have opened the way for a broader usage of DNN verification technology in many application areas, including safety-critical ones. However, DNN verifiers are themselves complex programs that have been shown to be susceptible to errors and numerical imprecision; this, in turn, has raised the question of trust in DNN verifiers. One prominent attempt to address this issue is enhancing DNN verifiers with the capability of producing certificates of their results that are subject to independent algorithmic checking. While formulations of Marabou certificate checking already exist on top of the state-of-the-art DNN verifier Marabou, they are implemented in C++, and that code itself raises the question of trust (e.g., in the precision of floating point calculations or guarantees for implementation soundness). Here, we present an alternative implementation of the Marabou certificate checking in Imandra - an industrial functional programming language and an interactive theorem prover (ITP) - that allows us to obtain full proof of certificate correctness. The significance of the result is two-fold. Firstly, it gives stronger independent guarantees for Marabou proofs. Secondly, it opens the way for the wider adoption of DNN verifiers in interactive theorem proving in the same way as many ITPs already incorporate SMT solvers.
Cite as

Remi Desmartin, Omri Isac, Grant Passmore, Ekaterina Komendantskaya, Kathrin Stark, and Guy Katz. A Certified Proof Checker for Deep Neural Network Verification in Imandra. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 1:1-1:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{desmartin_et_al:LIPIcs.ITP.2025.1,
  author =	{Desmartin, Remi and Isac, Omri and Passmore, Grant and Komendantskaya, Ekaterina and Stark, Kathrin and Katz, Guy},
  title =	{{A Certified Proof Checker for Deep Neural Network Verification in Imandra}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{1:1--1:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.1},
  URN =		{urn:nbn:de:0030-drops-246000},
  doi =		{10.4230/LIPIcs.ITP.2025.1},
  annote =	{Keywords: Neural Network Verification, Farkas Lemma, Proof Certification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.18
Formalising New Mathematics in Isabelle: Diagonal Ramsey

Authors: Lawrence C. Paulson

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
The formalisation of mathematics is becoming routine, but its value to research mathematicians remains unproven. There are few examples of using proof assistants to verify new work. This paper reports the formalisation - inspired by a Lean one by Bhavik Mehta - of a major new result [Marcelo Campos et al., 2023] about Ramsey numbers. One unexpected finding was a heavy role for computer algebra techniques.
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Lawrence C. Paulson. Formalising New Mathematics in Isabelle: Diagonal Ramsey. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{paulson:LIPIcs.ITP.2025.18,
  author =	{Paulson, Lawrence C.},
  title =	{{Formalising New Mathematics in Isabelle: Diagonal Ramsey}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.18},
  URN =		{urn:nbn:de:0030-drops-246163},
  doi =		{10.4230/LIPIcs.ITP.2025.18},
  annote =	{Keywords: Isabelle, formalisation of mathematics, Ramsey’s theorem, computer algebra}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.14
Canonical for Automated Theorem Proving in Lean

Authors: Chase Norman and Jeremy Avigad

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic supports higher-order and dependently-typed goals, structural recursion over indexed inductive types, and definitional equality. Canonical finds proofs for 84% of Natural Number Game problems in 51 seconds total.
Cite as

Chase Norman and Jeremy Avigad. Canonical for Automated Theorem Proving in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{norman_et_al:LIPIcs.ITP.2025.14,
  author =	{Norman, Chase and Avigad, Jeremy},
  title =	{{Canonical for Automated Theorem Proving in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.14},
  URN =		{urn:nbn:de:0030-drops-246128},
  doi =		{10.4230/LIPIcs.ITP.2025.14},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Proving, Dependent Type Theory, Inhabitation, Unification, Program Synthesis, Formal Methods}
}
Document
DOI: 10.4230/OASIcs.SpaceCHI.2025.1
Human-AI Interaction in Space: Insights from a Mars Analog Mission with the Harmony Large Language Model

Authors: Hippolyte Hilgers, Jean Vanderdonckt, and Radu-Daniel Vatavu

Published in: OASIcs, Volume 130, Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)

Abstract
The operational complexities of space missions require reliable, context-aware technical assistance for astronauts, especially when technical expertise is not available onboard and communication with Earth is delayed or limited. In this context, Large Language Models present a promising opportunity to augment human capabilities. To this end, we present Harmony, a model designed to provide astronauts with real-time technical assistance, fostering human-AI collaboration during analog missions. We report empirical results from an experiment involving seven analog astronauts that evaluated their user experience with Harmony in both a conventional environment and an isolated, confined, and extreme physical setting at the Mars Desert Research Station over four sessions, and discuss how the Mars analog environment impacted their experience. Our findings reveal the extent to which human-AI interactions evolve across various user experience dimensions and suggest how Harmony can be further adapted to suit extreme environments, with a focus on SpaceCHI.
Cite as

Hippolyte Hilgers, Jean Vanderdonckt, and Radu-Daniel Vatavu. Human-AI Interaction in Space: Insights from a Mars Analog Mission with the Harmony Large Language Model. In Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025). Open Access Series in Informatics (OASIcs), Volume 130, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hilgers_et_al:OASIcs.SpaceCHI.2025.1,
  author =	{Hilgers, Hippolyte and Vanderdonckt, Jean and Vatavu, Radu-Daniel},
  title =	{{Human-AI Interaction in Space: Insights from a Mars Analog Mission with the Harmony Large Language Model}},
  booktitle =	{Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)},
  pages =	{1:1--1:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-384-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{130},
  editor =	{Bensch, Leonie and Nilsson, Tommy and Nisser, Martin and Pataranutaporn, Pat and Schmidt, Albrecht and Sumini, Valentina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SpaceCHI.2025.1},
  URN =		{urn:nbn:de:0030-drops-239912},
  doi =		{10.4230/OASIcs.SpaceCHI.2025.1},
  annote =	{Keywords: Extreme user experience, Human-AI interaction, Isolated-confined-extreme environment, Interaction design, Large Language Models, Mars Desert Research Station, Space mission, Technical assistance, Technical documentation, User experience}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.27
A QPTAS for Facility Location on Unit Disk Graphs

Authors: Zachary Friggstad, Mohsen Rezapour, Mohammad R. Salavatipour, and Hao Sun

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We study the classic (Uncapacitated) Facility Location problem on Unit Disk Graphs (UDGs). For a given point set P in the plane, the unit disk graph UDG(P) on P has vertex set P and an edge between two distinct points p, q ∈ P if and only if their Euclidean distance |pq| is at most 1. The weight of the edge pq is equal to their distance |pq|. An instance of {Facility Location} on UDG(P) consists of a set C ⊆ P of clients and a set F ⊆ P of facilities, each having an opening cost f_i. The goal is to pick a subset F' ⊆ F to open while minimizing ∑_{i ∈ F'} f_i + ∑_{v ∈ C} d(v,F'), where d(v,F') is the distance of v to nearest facility in F' through UDG(P). In this paper, we present the first Quasi-Polynomial Time Approximation Schemes (QPTAS) for the problem. While approximation schemes are well-established for facility location problems on sparse geometric graphs (such as planar graphs), there is a lack of such results for dense graphs. Specifically, prior to this study, to the best of our knowledge, there was no approximation scheme for any facility location problem on UDGs in the general setting.
Cite as

Zachary Friggstad, Mohsen Rezapour, Mohammad R. Salavatipour, and Hao Sun. A QPTAS for Facility Location on Unit Disk Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friggstad_et_al:LIPIcs.WADS.2025.27,
  author =	{Friggstad, Zachary and Rezapour, Mohsen and Salavatipour, Mohammad R. and Sun, Hao},
  title =	{{A QPTAS for Facility Location on Unit Disk Graphs}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{27:1--27:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.27},
  URN =		{urn:nbn:de:0030-drops-242586},
  doi =		{10.4230/LIPIcs.WADS.2025.27},
  annote =	{Keywords: Facility Location, Unit Disk Graphs, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.4
Distributive Laws of Monadic Containers

Authors: Chris Purdy and Stefania Damato

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
Containers are used to carve out a class of strictly positive data types in terms of shapes and positions. They can be interpreted via a fully-faithful functor into endofunctors on Set. Monadic containers are those containers whose interpretation as a Set functor carries a monad structure. The category of containers is closed under container composition and is a monoidal category, whereas monadic containers do not in general compose. In this paper, we develop a characterisation of distributive laws of monadic containers. Distributive laws were introduced as a sufficient condition for the composition of the underlying functors of two monads to also carry a monad structure. Our development parallels Ahman and Uustalu’s characterisation of distributive laws of directed containers, i.e. containers whose Set functor interpretation carries a comonad structure. Furthermore, by combining our work with theirs, we construct characterisations of mixed distributive laws (i.e. of directed containers over monadic containers and vice versa), thereby completing the "zoo" of container characterisations of (co)monads and their distributive laws. We have found these characterisations amenable to development of existence and uniqueness proofs of distributive laws, particularly in the mechanised setting of Cubical Agda, in which most of the theory of this paper has been formalised.
Cite as

Chris Purdy and Stefania Damato. Distributive Laws of Monadic Containers. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{purdy_et_al:LIPIcs.CALCO.2025.4,
  author =	{Purdy, Chris and Damato, Stefania},
  title =	{{Distributive Laws of Monadic Containers}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.4},
  URN =		{urn:nbn:de:0030-drops-235633},
  doi =		{10.4230/LIPIcs.CALCO.2025.4},
  annote =	{Keywords: distributive laws, monadic containers, monads, dependent types, cubical agda}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2025.2
Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk)

Authors: Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Neuro-symbolic programs, i.e. programs containing both machine learning components and traditional symbolic code, are becoming increasingly widespread. Finding a general methodology for verifying such programs is challenging due to both the number of different tools involved and the intricate interface between the "neural" and "symbolic" program components. In this paper we present a general decomposition of the neuro-symbolic verification problem into parts, and examine the problem of the embedding gap that occurs when one tries to combine proofs about the neural and symbolic components. To address this problem we then introduce Vehicle - standing as an abbreviation for a "verification condition language" - an intermediate programming language interface between machine learning frameworks, automated theorem provers, and dependently-typed formalisations of neuro-symbolic programs. Vehicle allows users to specify the properties of the neural components of neuro-symbolic programs once, and then safely compile the specification to each interface using a tailored typing and compilation procedure. We give a high-level overview of Vehicle’s overall design, its interfaces and compilation & type-checking procedures, and then demonstrate its utility by formally verifying the safety of a simple autonomous car controlled by a neural network, operating in a stochastic environment with imperfect information.
Cite as

Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi. Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk). In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 2:1-2:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{daggitt_et_al:LIPIcs.FSCD.2025.2,
  author =	{Daggitt, Matthew L. and Kokke, Wen and Atkey, Robert and Komendantskaya, Ekaterina and Slusarz, Natalia and Arnaboldi, Luca},
  title =	{{Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{2:1--2:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.2},
  URN =		{urn:nbn:de:0030-drops-236172},
  doi =		{10.4230/LIPIcs.FSCD.2025.2},
  annote =	{Keywords: Neural Network Verification, Types, Interactive Theorem Provers}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2024.9
Complexity of Cubical Cofibration Logics I: coNP-Complete Examples

Authors: Robert Rose and Daniel R. Licata

Published in: LIPIcs, Volume 336, 30th International Conference on Types for Proofs and Programs (TYPES 2024)

Abstract
We provide a comprehensive classification of the cofibration entailment problem, COFENT, for the cofibration logics of various cubical type theories in use today. The problem COFENT arose from the need of cubical proof assistants to automate reasoning about cubical complexes included in an n-dimensional hypercube. Intuitively, it asks: given logical descriptions of two such complexes, is one a subcomplex of the other? We show that the common variants of COFENT are coNP-complete.
Cite as

Robert Rose and Daniel R. Licata. Complexity of Cubical Cofibration Logics I: coNP-Complete Examples. In 30th International Conference on Types for Proofs and Programs (TYPES 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 336, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rose_et_al:LIPIcs.TYPES.2024.9,
  author =	{Rose, Robert and Licata, Daniel R.},
  title =	{{Complexity of Cubical Cofibration Logics I: coNP-Complete Examples}},
  booktitle =	{30th International Conference on Types for Proofs and Programs (TYPES 2024)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-376-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{336},
  editor =	{M{\o}gelberg, Rasmus Ejlers and van den Berg, Benno},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2024.9},
  URN =		{urn:nbn:de:0030-drops-233711},
  doi =		{10.4230/LIPIcs.TYPES.2024.9},
  annote =	{Keywords: cubical sets, internal language, intuitionistic logic, dependent type theory, homotopy type theory, decision procedures}
}
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