35 Search Results for "Das, Anupam"

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.CSL.2026.15
Cyclic Proof Theory of Generalised Inductive Definitions

Authors: Gianluca Curzi and Lukas Melgaard

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

Abstract
We study cyclic proof systems for μPA, an extension of Peano arithmetic by generalised inductive definitions that is arithmetically equivalent to the (impredicative) subsystem of second-order arithmetic Π^1_2-CA₀ by Möllerfeld. The main result of this paper is that cyclic and inductive μPA have the same proof-theoretic strength. First, we translate cyclic proofs into an annotated variant based on Sprenger and Dam’s systems for first-order μ-calculus, whose stronger validity condition allows for a simpler proof of soundness. We then formalise this argument within Π^1_2-CA₀, leveraging Möllerfeld’s conservativity properties. To this end, we build on prior work by Curzi and Das on the reverse mathematics of the Knaster-Tarski theorem. As a byproduct of our proof methods we show that, despite the stronger validity condition, annotated and "plain" cyclic proofs for μPA prove the same theorems. This work represents a further step in the non-wellfounded proof-theoretic analysis of theories of arithmetic via impredicative fragments of second-order arithmetic, an approach initiated by Simpson’s Cyclic Arithmetic, and continued by Das and Melgaard in the context of arithmetical inductive definitions.
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Gianluca Curzi and Lukas Melgaard. Cyclic Proof Theory of Generalised Inductive Definitions. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{curzi_et_al:LIPIcs.CSL.2026.15,
  author =	{Curzi, Gianluca and Melgaard, Lukas},
  title =	{{Cyclic Proof Theory of Generalised Inductive Definitions}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{15:1--15:19},
  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.2026.15},
  URN =		{urn:nbn:de:0030-drops-254399},
  doi =		{10.4230/LIPIcs.CSL.2026.15},
  annote =	{Keywords: cyclic proofs, positive inductive definitions, arithmetic, fixed points, proof theory, reset proof systems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.80
FPT Approximations for Connected Maximum Coverage

Authors: Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi

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

Abstract
We revisit connectivity-constrained coverage through a unifying model, Partial Connected Red-Blue Dominating Set (PartialConRBDS). Given a bipartite graph G = (R∪ B,E) with red vertices R and blue vertices B, an auxiliary connectivity graph G_{conn} on R, and integers k,t, the task is to find a set S ⊆ R with |S| ≤ k such that G_{conn}[S] is connected and S dominates at least t blue vertices. This formulation captures connected variants of Maximum Coverage [Hochbaum-Rao, Inf. Proc. Lett., 2020; D'Angelo-Delfaraz, AAMAS 2025], Partial Vertex Cover, and Partial Dominating Set [Khuller et al., SODA 2014; Lamprou et al., TCS 2021] via standard encodings. Limits to parameterized tractability. PartialConRBDS is W[1]-hard parameterized by k even under strong restrictions: it remains hard when G_{conn} is a clique or a star and the incidence graph G is 3-degenerate, or when G is K_{2,2}-free. Inapproximability. For every ε > 0, there is no polynomial-time (1, 1-1/e+ε)-approximation unless 𝖯 = NP. Moreover, under ETH, no algorithm running in f(k)⋅ n^{o(k)} time achieves an g(k)-approximation for k for any computable function g(⋅), or for any ε > 0, a (1-1/e+ε)-approximation for t. Graphical special cases. Partial Connected Dominating Set is W[2]-hard parameterized by k and inherits the same ETH-based f(k)⋅ n^{o(k)} inapproximability bound as above; Partial Connected Vertex Cover is W[1]-hard parameterized by k. These hardness boundaries delineate a natural "sweet spot" for study: within appropriate structural restrictions on the incidence graph, one can still aim for fine-grained (FPT) approximations. Our algorithms. We solve PartialConRBDS exactly by reducing it to Relaxed Directed Steiner Out-Tree in time (2e)^t ⋅ n^{𝒪(1)}. For biclique-free incidences (i.e., when G excludes K_{d,d} as an induced subgraph), we obtain two complementary parameterized schemes: - An Efficient Parameterized Approximation Scheme (EPAS) running in time 2^{𝒪(k² d/ε)}⋅ n^{𝒪(1)} that either returns a connected solution of size at most k covering at least (1-ε)t blue vertices, or correctly reports that no connected size-k solution covers t; and - A Parameterized Approximation Scheme (PAS) running in time 2^{𝒪(kd(k²+log d))}⋅ n^{𝒪(1/ε)} that either returns a connected solution of size at most (1+ε)k covering at least t blue vertices, or correctly reports that no connected size-k solution covers t. Together, these results chart the boundary between hardness and FPT-approximability for connectivity-constrained coverage.
Cite as

Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. FPT Approximations for Connected Maximum Coverage. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 80:1-80:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{inamdar_et_al:LIPIcs.ITCS.2026.80,
  author =	{Inamdar, Tanmay and Jana, Satyabrata and Kundu, Madhumita and Lokshtanov, Daniel and Saurabh, Saket and Zehavi, Meirav},
  title =	{{FPT Approximations for Connected Maximum Coverage}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{80:1--80:24},
  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.2026.80},
  URN =		{urn:nbn:de:0030-drops-253674},
  doi =		{10.4230/LIPIcs.ITCS.2026.80},
  annote =	{Keywords: Partial Dominating Set, Connectivity, Maximum Coverage, FPT Approximation, Fixed-parameter Tractability}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.38
Lower Bounds on Tree Covers

Authors: Yu Chen, Zihan Tan, and Hangyu Xu

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

Abstract
Given an n-point metric space (X,d_X), a tree cover 𝒯 is a set of |𝒯| = k trees on X such that every pair of vertices in X has a low-distortion path in one of the trees in 𝒯. Tree covers have been playing a crucial role in graph algorithms for decades, and the research focus is the construction of tree covers with small size k and distortion. When k = 1, the best distortion is known to be Θ(n). For a constant k ≥ 2, the best distortion upper bound is Õ(n^{1/k}) and the strongest lower bound is Ω(log_k n), leaving a gap to be closed. In this paper, we improve the lower bound to Ω(n^{1/(2^{k-1)}}). Our proof is a novel analysis on a structurally simple grid-like graph, which utilizes some combinatorial fixed-point theorems. We believe that they will prove useful for analyzing other tree-like data structures as well.
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Yu Chen, Zihan Tan, and Hangyu Xu. Lower Bounds on Tree Covers. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2026.38,
  author =	{Chen, Yu and Tan, Zihan and Xu, Hangyu},
  title =	{{Lower Bounds on Tree Covers}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{38:1--38:16},
  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.2026.38},
  URN =		{urn:nbn:de:0030-drops-253254},
  doi =		{10.4230/LIPIcs.ITCS.2026.38},
  annote =	{Keywords: Tree Covers, Combinatorial Fixed-Point Theorems}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.40
On the Randomized Locality of Matching Problems in Regular Graphs

Authors: Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang

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

Abstract
The main goal in distributed symmetry-breaking is to understand the locality of problems: the radius of the neighborhood that a node must explore to determine its part of a global solution. In this work, we study the locality of matching problems in the family of regular graphs, which is one of the main benchmarks for establishing lower bounds on the locality of symmetry-breaking problems, as well as for obtaining classification results. Our main results are summarized as follows: 1) Approximate matching: We develop randomized algorithms to show that (1 + ε)-approximate matching in regular graphs is truly local, i.e., the locality depends only on ε and is independent of all other graph parameters. Furthermore, as long as the degree Δ is not very small (namely, as long as Δ ≥ poly(1/ε)), this dependence is only logarithmic in 1/ε. This stands in sharp contrast to maximal matching in regular graphs which requires some dependence on the number of nodes n or the degree Δ. 2) Maximal matching: Our techniques further allow us to establish a strong separation between the node-averaged complexity and worst-case complexity of maximal matching in regular graphs, by showing that the former is only O(1). Central to our main technical contribution is a novel martingale-based analysis for the ≈ 40-year-old algorithm by Luby. In particular, our analysis shows that applying one round of Luby’s algorithm on the line graph of a Δ-regular graph results in an almost Δ/2-regular graph.
Cite as

Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang. On the Randomized Locality of Matching Problems in Regular Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 40:1-40:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khoury_et_al:LIPIcs.DISC.2025.40,
  author =	{Khoury, Seri and Purohit, Manish and Schild, Aaron and Wang, Joshua R.},
  title =	{{On the Randomized Locality of Matching Problems in Regular Graphs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{40:1--40:20},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-248570},
  doi =		{10.4230/LIPIcs.DISC.2025.40},
  annote =	{Keywords: regular graphs, maximum matching, augmenting paths, distributed algorithms, Luby’s algorithm, martingales}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.25
Model-Agnostic Approximation of Constrained Forest Problems

Authors: Corinna Coupette, Alipasha Montaseri, and Christoph Lenzen

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

Abstract
Constrained Forest Problems (CFPs) as introduced by Goemans and Williamson in 1995 capture a wide range of network design problems with edge subsets as solutions, such as Minimum Spanning Tree, Steiner Forest, and Point-to-Point Connection. While individual CFPs have been studied extensively in individual computational models, a unified approach to solving general CFPs in multiple computational models has been lacking. Against this background, we present the shell-decomposition algorithm, a model-agnostic meta-algorithm that efficiently computes a (2+ε)-approximation to CFPs for a broad class of forest functions. The shell-decomposition algorithm isolates the problem-specific hardness of individual CFPs in a single computational subroutine, breaking the remainder of the computation into fundamental tasks that are studied extensively in a wide range of computational models. In contrast to prior work, our framework is compatible with the use of approximate distances. To demonstrate the power and flexibility of this result, we instantiate our algorithm for three fundamental, NP-hard CFPs (Steiner Forest, Point-to-Point Connection, and Facility Placement and Connection) in three different computational models (Congest, PRAM, and Multi-Pass Streaming). For constant ε, we obtain the following (2+ε)-approximations in the Congest model: [(1)] 1) For Steiner Forest specified via input components (SF-IC), where each node knows the identifier of one of k disjoint subsets of V (the input components), we achieve a deterministic (2+ε)-approximation in 𝒪̃(√n+D+k) rounds, where D is the hop diameter of the graph, significantly improving over the state of the art. 2) For Steiner Forest specified via symmetric connection requests (SF-SCR), where connection requests are issued to pairs of nodes u,v ∈ V, we leverage randomized equality testing to reduce the running time to 𝒪̃(√n+D), succeeding with high probability. 3) For Point-to-Point Connection, we provide a (2+ε)-approximation in 𝒪̃(√n+D) rounds. 4) For Facility Placement and Connection, a relative of non-metric Uncapacitated Facility Location, we obtain a (2+ε)-approximation in 𝒪̃(√n + D) rounds. We further show how to replace the √n+D term by the complexity of solving Partwise Aggregation, achieving (near-)universal optimality in any setting in which a solution to Partwise Aggregation in near-shortcut-quality time is known. Notably, all of our concrete results can be derived with relative ease once our model-agnostic meta-algorithm has been specified. This demonstrates the power of our modularization approach to algorithm design.
Cite as

Corinna Coupette, Alipasha Montaseri, and Christoph Lenzen. Model-Agnostic Approximation of Constrained Forest Problems. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 25:1-25:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{coupette_et_al:LIPIcs.DISC.2025.25,
  author =	{Coupette, Corinna and Montaseri, Alipasha and Lenzen, Christoph},
  title =	{{Model-Agnostic Approximation of Constrained Forest Problems}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{25:1--25:24},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-248420},
  doi =		{10.4230/LIPIcs.DISC.2025.25},
  annote =	{Keywords: Distributed Graph Algorithms, Model-Agnostic Algorithms, Steiner Forest}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.39
Right-Linear Lattices: An Algebraic Theory of ω-Regular Languages, with Fixed Points

Authors: Anupam Das and Abhishek De

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely unexplored. In recent work [Anupam Das and Abhishek De, 2024], a notation for non-deterministic finite automata (NFAs) was introduced, along with a sound and complete axiomatisation of their equational theory via right-linear algebras. In this paper, we extend that line of work to the setting of infinite words. In particular, we present a dualised syntax, yielding a notation for APAs based on right-linear lattice expressions, and provide a natural axiomatisation of their equational theory with respect to the standard language model of ω-regular languages. The design of this axiomatisation is guided by the theory of fixed point logics; in fact, the completeness factors cleanly through the completeness of the linear-time μ-calculus.
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Anupam Das and Abhishek De. Right-Linear Lattices: An Algebraic Theory of ω-Regular Languages, with Fixed Points. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{das_et_al:LIPIcs.MFCS.2025.39,
  author =	{Das, Anupam and De, Abhishek},
  title =	{{Right-Linear Lattices: An Algebraic Theory of \omega-Regular Languages, with Fixed Points}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.39},
  URN =		{urn:nbn:de:0030-drops-241461},
  doi =		{10.4230/LIPIcs.MFCS.2025.39},
  annote =	{Keywords: omega-languages, regular languages, fixed points, Kleene algebras, right-linear grammars}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.32
Interpolation as Cut-Introduction: On the Computational Content of Craig-Lyndon Interpolation

Authors: Alexis Saurin

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

Abstract
Analyzing Maehara’s method for proving Craig’s interpolation theorem, we extract a "proof relevant" interpolation theorem for first-order LL in the sense that if π is a cut-free sequent proof of A⊢ B, we can find a formula C in the common vocabulary of A and B and proofs π₁,π₂ of A⊢ C and C⊢ B respectively such that π₁ composed with π₂ cut-reduces to π. As a direct corollary, we get similar proof relevant interpolation results for LJ and LK using linear translations. This refined interpolation is then rephrased in terms of a cut-introduction process synthetizing the interpolant. Finally, we analyze the computational content of interpolation by proving an interpolation result for Curien and Herbelin’s Duality of Computation.
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Alexis Saurin. Interpolation as Cut-Introduction: On the Computational Content of Craig-Lyndon Interpolation. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{saurin:LIPIcs.FSCD.2025.32,
  author =	{Saurin, Alexis},
  title =	{{Interpolation as Cut-Introduction: On the Computational Content of Craig-Lyndon Interpolation}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{32:1--32:21},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-236478},
  doi =		{10.4230/LIPIcs.FSCD.2025.32},
  annote =	{Keywords: Classical Logic, Interpolation, Cut Elimination, Linear Logic, Sequent calculus, System L}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.53
Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs

Authors: Yu Chen and Zihan Tan

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study vertex sparsification for preserving cuts. Given a graph G with a subset |T| = k of its vertices called terminals, a quality-q cut sparsifier is a graph G' that contains T, such that, for any partition (T₁,T₂) of T into non-empty subsets, the value of the min-cut in G' separating T₁ from T₂ is within factor q from the value of the min-cut in G separating T₁ from T₂. The construction of cut sparsifiers with good (small) quality and size has been a central problem in graph compression for years. Planar graphs and quasi-bipartite graphs are two important special families studied in this research direction. The main results in this paper are new cut sparsifier constructions for them in the high-quality regime (where q = 1 or 1+{ε} for small {ε} > 0). We first show that every planar graph admits a planar quality-(1+{ε}) cut sparsifier of size Õ(k/poly({ε})), which is in sharp contrast with the lower bound of 2^{Ω(k)} for the quality-1 case. We then show that every quasi-bipartite graph admits a quality-1 cut sparsifier of size 2^{Õ(k²)}. This is the second to improve over the doubly-exponential bound for general graphs (previously only planar graphs have been shown to have single-exponential size quality-1 cut sparsifiers). Lastly, we show that contraction, a common approach for constructing cut sparsifiers adopted in most previous works, does not always give optimal bounds for cut sparsifiers. We demonstrate this by showing that the optimal size bound for quality-(1+{ε}) contraction-based cut sparsifiers for quasi-bipartite graphs lies in the range [k^{̃Ω(1/{ε})},k^{O(1/{ε}²)}], while in previous work an upper bound of Õ(k/{ε}²) was achieved via a non-contraction approach.
Cite as

Yu Chen and Zihan Tan. Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 53:1-53:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.53,
  author =	{Chen, Yu and Tan, Zihan},
  title =	{{Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{53:1--53:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.53},
  URN =		{urn:nbn:de:0030-drops-234304},
  doi =		{10.4230/LIPIcs.ICALP.2025.53},
  annote =	{Keywords: Termianl Cut, Graph Sparsification}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.50
New Results on a General Class of Minimum Norm Optimization Problems

Authors: Kuowen Chen, Jian Li, Yuval Rabani, and Yiran Zhang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the general norm optimization for combinatorial problems, initiated by Chakrabarty and Swamy (STOC 2019). We propose a general formulation that captures a large class of combinatorial structures: we are given a set 𝒰 of n weighted elements and a family of feasible subsets ℱ. Each subset S ∈ ℱ is called a feasible solution/set of the problem. We denote the value vector by v = {v_i}_{i ∈ [n]}, where v_i ≥ 0 is the value of element i. For any subset S ⊆ 𝒰, we use v[S] to denote the n-dimensional vector {v_e⋅ 𝟏[e ∈ S]}_{e ∈ 𝒰} (i.e., we zero out all entries that are not in S). Let f: ℝⁿ → ℝ_+ be a symmetric monotone norm function. Our goal is to minimize the norm objective f(v[S]) over feasible subset S ∈ ℱ. The problem significantly generalizes the corresponding min-sum and min-max problems. We present a general equivalent reduction of the norm minimization problem to a multi-criteria optimization problem with logarithmic budget constraints, up to a constant approximation factor. Leveraging this reduction, we obtain constant factor approximation algorithms for the norm minimization versions of several covering problems, such as interval cover, multi-dimensional knapsack cover, and logarithmic factor approximation for set cover. We also study the norm minimization versions for perfect matching, s-t path and s-t cut. We show the natural linear programming relaxations for these problems have a large integrality gap. To complement the negative result, we show that, for perfect matching, it is possible to obtain a bi-criteria result: for any constant ε,δ > 0, we can find in polynomial time a nearly perfect matching (i.e., a matching that matches at least 1-ε proportion of vertices) and its cost is at most (8+δ) times of the optimum for perfect matching. Moreover, we establish the existence of a polynomial-time O(log log n)-approximation algorithm for the norm minimization variant of the s-t path problem. Specifically, our algorithm achieves an α-approximation with a time complexity of n^{O(log log n / α)}, where 9 ≤ α ≤ log log n.
Cite as

Kuowen Chen, Jian Li, Yuval Rabani, and Yiran Zhang. New Results on a General Class of Minimum Norm Optimization Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.50,
  author =	{Chen, Kuowen and Li, Jian and Rabani, Yuval and Zhang, Yiran},
  title =	{{New Results on a General Class of Minimum Norm Optimization Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{50:1--50:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.50},
  URN =		{urn:nbn:de:0030-drops-234276},
  doi =		{10.4230/LIPIcs.ICALP.2025.50},
  annote =	{Keywords: Approximation Algorithms, Minimum Norm Optimization, Linear Programming}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.30
Light Spanners with Small Hop-Diameter

Authors: Sujoy Bhore and Lazar Milenković

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Lightness, sparsity, and hop-diameter are the fundamental parameters of geometric spanners. Arya et al. [STOC'95] showed in their seminal work that there exists a construction of Euclidean (1+ε)-spanners with hop-diameter O(log n) and lightness O(log n). They also gave a general tradeoff of hop-diameter k and sparsity O(α_k(n)), where α_k is a very slowly growing inverse of an Ackermann-style function. The former combination of logarithmic hop-diameter and lightness is optimal due to the lower bound by Dinitz et al. [FOCS'08]. Later, Elkin and Solomon [STOC'13] generalized the light spanner construction to doubling metrics and extended the tradeoff for more values of hop-diameter k. In a recent line of work [SoCG'22, SoCG'23], Le et al. proved that the aforementioned tradeoff between the hop-diameter and sparsity is tight for every choice of hop-diameter k. A fundamental question remains: What is the optimal tradeoff between the hop-diameter and lightness for every value of k? In this paper, we present a general framework for constructing light spanners with small hop-diameter. Our framework is based on tree covers. In particular, we show that if a metric admits a tree cover with γ trees, stretch t, and lightness L, then it also admits a t-spanner with hop-diameter k and lightness O(kn^{2/k}⋅ γ L). Further, we note that the tradeoff for trees is tight due to a construction in uniform line metric, which is perhaps the simplest tree metric. As a direct consequence of this framework, we obtain new tradeoffs between lightness and hop-diameter for doubling metrics.
Cite as

Sujoy Bhore and Lazar Milenković. Light Spanners with Small Hop-Diameter. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhore_et_al:LIPIcs.ICALP.2025.30,
  author =	{Bhore, Sujoy and Milenkovi\'{c}, Lazar},
  title =	{{Light Spanners with Small Hop-Diameter}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.30},
  URN =		{urn:nbn:de:0030-drops-234075},
  doi =		{10.4230/LIPIcs.ICALP.2025.30},
  annote =	{Keywords: Geometric Spanners, Lightness, Hop-Diameter, Recurrences, Lower Bounds}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.69
Approximation Algorithms for Optimal Hopsets

Authors: Michael Dinitz, Ama Koranteng, and Yasamin Nazari

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
For a given graph G, a hopset H with hopbound β and stretch α is a set of edges such that between every pair of vertices u and v, there is a path with at most β hops in G ∪ H that approximates the distance between u and v up to a multiplicative stretch of α. Hopsets have found a wide range of applications for distance-based problems in various computational models since the 90s. More recently, there has been significant interest in understanding these fundamental objects from an existential and structural perspective. But all of this work takes a worst-case (or existential) point of view: How many edges do we need to add to satisfy a given hopbound and stretch requirement for any input graph? We initiate the study of the natural optimization variant of this problem: given a specific graph instance, what is the minimum number of edges that satisfy the hopbound and stretch requirements? We give approximation algorithms for a generalized hopset problem which, when combined with known existential bounds, lead to different approximation guarantees for various regimes depending on hopbound, stretch, and directed vs. undirected inputs. We complement our upper bounds with a lower bound that implies Label Cover hardness for directed hopsets and shortcut sets with hopbound at least 3.
Cite as

Michael Dinitz, Ama Koranteng, and Yasamin Nazari. Approximation Algorithms for Optimal Hopsets. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dinitz_et_al:LIPIcs.ICALP.2025.69,
  author =	{Dinitz, Michael and Koranteng, Ama and Nazari, Yasamin},
  title =	{{Approximation Algorithms for Optimal Hopsets}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{69:1--69:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.69},
  URN =		{urn:nbn:de:0030-drops-234464},
  doi =		{10.4230/LIPIcs.ICALP.2025.69},
  annote =	{Keywords: Hopsets, Approximation Algorithms}
}
Document
Resource
DOI: 10.4230/TGDK.3.1.1
KG2Tables: A Domain-Specific Tabular Data Generator to Evaluate Semantic Table Interpretation Systems

Authors: Nora Abdelmageed, Ernesto Jiménez-Ruiz, Oktie Hassanzadeh, and Birgitta König-Ries

Published in: TGDK, Volume 3, Issue 1 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 1

Abstract
Tabular data, often in the form of CSV files, plays a pivotal role in data analytics pipelines. Understanding this data semantically, known as Semantic Table Interpretation (STI), is crucial but poses challenges due to several factors such as the ambiguity of labels. As a result, STI has gained increasing attention from the community in the past few years. Evaluating STI systems requires well-established benchmarks. Most of the existing large-scale benchmarks are derived from general domain sources and focus on ambiguity, while domain-specific benchmarks are relatively small in size. This paper introduces KG2Tables, a framework that can construct domain-specific large-scale benchmarks from a Knowledge Graph (KG). KG2Tables leverages the internal hierarchy of the relevant KG concepts and their properties. As a proof of concept, we have built large datasets in the food, biodiversity, and biomedical domains. The resulting datasets, tFood, tBiomed, and tBiodiv, have been made available for the public in the ISWC SemTab challenge (2023 and 2024 editions). We include the evaluation results of top-performing STI systems using tFood Such results underscore its potential as a robust evaluation benchmark for challenging STI systems. We demonstrate the data quality level using a sample-based approach for the generated benchmarks including, for example, realistic tables assessment. Nevertheless, we provide an extensive discussion of KG2Tables explaining how it could be used to create other benchmarks from any domain of interest and including its key features and limitations with suggestions to overcome them.
Cite as

Nora Abdelmageed, Ernesto Jiménez-Ruiz, Oktie Hassanzadeh, and Birgitta König-Ries. KG2Tables: A Domain-Specific Tabular Data Generator to Evaluate Semantic Table Interpretation Systems. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 1, pp. 1:1-1:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{abdelmageed_et_al:TGDK.3.1.1,
  author =	{Abdelmageed, Nora and Jim\'{e}nez-Ruiz, Ernesto and Hassanzadeh, Oktie and K\"{o}nig-Ries, Birgitta},
  title =	{{KG2Tables: A Domain-Specific Tabular Data Generator to Evaluate Semantic Table Interpretation Systems}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:28},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.1.1},
  URN =		{urn:nbn:de:0030-drops-230104},
  doi =		{10.4230/TGDK.3.1.1},
  annote =	{Keywords: Semantic Table Interpretation (STI), Knowledge Graph (KG), STI Benchmark, Food, Biodiversity, Biomedical}
}
Document
DOI: 10.4230/DagRep.14.8.1
Proof Representations: From Theory to Applications (Dagstuhl Seminar 24341)

Authors: Anupam Das, Elaine Pimentel, Lutz Straßburger, and Robin Martinot

Published in: Dagstuhl Reports, Volume 14, Issue 8 (2025)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 24341 "Proof Representations: From Theory to Applications". Proof theory is the study of formal proofs as mathematical objects in their own right. The subject has enjoyed continued attention among computer scientists in particular due to its significance for formalization, metalogic, and automation. In recent decades there has been a surge of interest on the representations of formal proofs themselves. The outcomes of these investigations have been remarkable, in particular extending the scope of structural proof theory to novel and richer settings: Richer line structures (e.g. hypersequents, nested sequents, labelled sequents) have resulted in a uniform treatment of standard modal logics, streamlining their metatheory and providing new tools for metalogical problems. Richer proof structures (e.g., cyclic proofs, annotated systems, infinitely branching proofs) have significantly advanced our understanding of fixed points and (co)induction. Indeed, we are now seeing many of these previously disjoint techniques being combined to push the boundaries of proof theoretic approaches to computational logic. Graphical proof representations (e.g., proof nets, atomic flows, combinatorial proofs) originating from "linear" logics, now not only comprise a well-behaved computational model for resource-sensitive reasoning, but also provide an impressively uniform treatment for logics across the board. In fact, we are now seeing many of these previously disjoint techniques being combined to push the boundaries of proof theoretic approaches to computational logic, which has produced deep and fruitful cross-fertilizations between programming languages and proof theory. Arguably, the most well-known is the Curry-Howard correspondence ("propositions-as-types") where (functional) programs correspond to formal proofs and their execution to normalization. A complementary tradition, proof-search-as-computation ("propositions-as-processes"), instead interprets (logic) programs to formulas and their execution to proof search. The goal of this Dagstuhl Seminar was twofold. First and foremost, we aimed to bring together theorists and practitioners exploiting proof representations to identify new directions of application and, simultaneously, distill new theoretical directions from problems "in the wild". At the same time, this seminar was intended to expose the interface between the proof-normalization and proof-search traditions by probing proof representations from both directions.
Cite as

Anupam Das, Elaine Pimentel, Lutz Straßburger, and Robin Martinot. Proof Representations: From Theory to Applications (Dagstuhl Seminar 24341). In Dagstuhl Reports, Volume 14, Issue 8, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{das_et_al:DagRep.14.8.1,
  author =	{Das, Anupam and Pimentel, Elaine and Stra{\ss}burger, Lutz and Martinot, Robin},
  title =	{{Proof Representations: From Theory to Applications (Dagstuhl Seminar 24341)}},
  pages =	{1--23},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{14},
  number =	{8},
  editor =	{Das, Anupam and Pimentel, Elaine and Stra{\ss}burger, Lutz and Martinot, Robin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.14.8.1},
  URN =		{urn:nbn:de:0030-drops-229975},
  doi =		{10.4230/DagRep.14.8.1},
  annote =	{Keywords: proof theory, proof calculi, computational interpretations, proof semantics, dynamic operators}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2025.3
Algebras for Automata: Reasoning with Regularity (Invited Talk)

Authors: Anupam Das

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In the second half of the 20th century various theories of regular expressions were proposed, eventually leading to the notion of a Kleene Algebra (KA). Kozen and Krob independently proved the completeness of KA for the model of regular languages, a now celebrated result that has been refined and generalised over the years. In recent years proof theoretic approaches to regular languages have been studied, providing alternative routes to metalogical results like completeness and decidability. In this talk I will present a new approach from a different starting point: finite state automata. A notation for non-deterministic finite automata is readily obtained via expressions with least fixed points, leading to a theory of right-linear algebras (RLA). RLA is strictly more general than KA, e.g. admitting ω-regular languages as a model too, and enjoys a simpler proof theory than KA. This allows us to recover (more general) metalogical results in a robust way, combining techniques from automata, games, and cyclic proofs. Finally I will discuss extensions of RLA by greatest fixed points, comprising a notation for parity automata, to reason about ω-regular languages too. This talk is based on joint works with Abhishek De [Anupam Das and Abhishek De, 2024a and 2024b].
Cite as

Anupam Das. Algebras for Automata: Reasoning with Regularity (Invited Talk). In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{das:LIPIcs.STACS.2025.3,
  author =	{Das, Anupam},
  title =	{{Algebras for Automata: Reasoning with Regularity}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.3},
  URN =		{urn:nbn:de:0030-drops-228281},
  doi =		{10.4230/LIPIcs.STACS.2025.3},
  annote =	{Keywords: Regular languages, Linear grammars, Proof theory, Cyclic proofs, Automata theory, Fixed points, Games}
}
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