36 Search Results for "Harel, David"

Document
DOI: 10.4230/LIPIcs.CPM.2026.3
Computing k-mers in Graphs

Authors: Jarno N. Alanko and Máximo Pérez-López

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
We initiate the study of computational problems on k-mers (strings of length k) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct k-mers found on the walks of a graph. We establish that this is #P-hard, even on connected deterministic DAGs. However, in the class of deterministic Wheeler graphs (Gagie, Manzini, and Sirén, TCS 2017), we show that distinct k-mers of such a graph W = (V, E) can be counted using O(|W|k) or O(n⁴ log k) arithmetic operations, where n = |V|, m = |E| and |W| = n+m. The latter result uses a new generalization of the technique of prefix doubling to Wheeler graphs. To generalize our results beyond Wheeler graphs, we discuss ways to transform a graph into a Wheeler graph in a manner that preserves the k-mers. As an application of our k-mer counting algorithms, we construct a representation of the de Bruijn graph of the k-mers that occupies O(n_k + |W|k log(max_{1 ≤ 𝓁 ≤ k} n_𝓁) + σlog m) bits of space, where n_𝓁 is the number of distinct 𝓁-mers in the Wheeler graph, and σ is the size of the alphabet. We show how to construct it in the same time complexity. Given that the Wheeler graph can be exponentially smaller than the de Bruijn graph, for large k this provides a theoretical improvement over previous de Bruijn graph construction methods from graphs, which must spend Ω(k) time per k-mer in the graph.
Cite as

Jarno N. Alanko and Máximo Pérez-López. Computing k-mers in Graphs. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alanko_et_al:LIPIcs.CPM.2026.3,
  author =	{Alanko, Jarno N. and P\'{e}rez-L\'{o}pez, M\'{a}ximo},
  title =	{{Computing k-mers in Graphs}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.3},
  URN =		{urn:nbn:de:0030-drops-259294},
  doi =		{10.4230/LIPIcs.CPM.2026.3},
  annote =	{Keywords: Wheeler graph, Wheeler language, de Bruijn graph, graph, k-mer, q-gram, DFA, #P-hard}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.30
Parallel Algorithms for Group Isomorphism via Code Equivalence

Authors: Michael Levet

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
In this paper, we exhibit AC³ isomorphism tests for coprime extensions H ⋉ N where H is elementary Abelian and N is Abelian; and groups where Rad(G) = Z(G) is elementary Abelian and G = Soc^{*}(G). The fact that isomorphism testing for these families is in P was established respectively by Qiao, Sarma, and Tang (STACS 2011), and Grochow and Qiao (CCC 2014, SIAM J. Comput. 2017). The polynomial-time isomorphism tests for both of these families crucially leveraged small (size O(log |G|)) instances of Linear Code Equivalence (Babai, SODA 2011). Here, we combine Luks' group-theoretic method for Graph Isomorphism (FOCS 1980, J. Comput. Syst. Sci. 1982) with the fact that G is given by its multiplication table, to implement the corresponding instances of Linear Code Equivalence in AC³. As a byproduct of our work, we show that isomorphism testing of arbitrary central-radical groups is decidable using AC circuits of depth O(log³ n) and size n^{O(log log n)}. This improves upon the previous bound of n^{O(log log n)}-time due to Grochow and Qiao (ibid.).
Cite as

Michael Levet. Parallel Algorithms for Group Isomorphism via Code Equivalence. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{levet:LIPIcs.SWAT.2026.30,
  author =	{Levet, Michael},
  title =	{{Parallel Algorithms for Group Isomorphism via Code Equivalence}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.30},
  URN =		{urn:nbn:de:0030-drops-260660},
  doi =		{10.4230/LIPIcs.SWAT.2026.30},
  annote =	{Keywords: Group Isomorphism, Circuit Complexity, Code Equivalence}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2026.1
Query Languages for Machine-Learning Models (Invited Talk)

Authors: Martin Grohe

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In my invited talk and this accompanying paper, I discuss two logics for weighted finite structures: first-order logic with summation (FO(SUM)) and its recursive extension IFP(SUM). These logics originate from foundational work by Grädel, Gurevich, and Meer in the 1990s. In recent joint work with Standke, Steegmans, and Van den Bussche, we have investigated these logics as query languages for machine learning models, specifically neural networks, which are naturally represented as weighted graphs. I present illustrative examples of queries to neural networks that can be expressed in these logics and discuss fundamental results on their expressiveness and computational complexity.
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Martin Grohe. Query Languages for Machine-Learning Models (Invited Talk). In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grohe:LIPIcs.STACS.2026.1,
  author =	{Grohe, Martin},
  title =	{{Query Languages for Machine-Learning Models}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.1},
  URN =		{urn:nbn:de:0030-drops-254904},
  doi =		{10.4230/LIPIcs.STACS.2026.1},
  annote =	{Keywords: Expressive power of query languages, fixed-point logics, weighted structures, neural networks, explainable AI}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.30
Reward Interfaces with Best-Effort Implementations

Authors: Rafael Dewes and Rayna Dimitrova

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

Abstract
Interface theories, notably interface automata, serve as expressive frameworks for component-based design, specifying component behavior and interaction in concurrent systems. Traditional interface formalisms specify assumptions that a component’s environment must satisfy and the guarantees that each component provides. This qualitative view of component interaction based on imposing strict assumptions and Boolean guarantees may, however, not be expressive enough to capture the system’s allowed or desired behaviors under different environments. In this paper, we introduce reward interfaces to support component-based design while accommodating multi-valued correctness requirements and adaptive best-effort satisfaction of component’s guarantees. Building upon interface automata, our framework enables modeling a rich class of quantitative component specifications. We propose formal notions of implementation, refinement and compatibility for reward interfaces. We study a class of reward interfaces with automata-based representations, for which we provide algorithms for checking compatibility and refinement, and existence of best-effort implementations. Our framework offers a comprehensive approach to reward interface specification and design.
Cite as

Rafael Dewes and Rayna Dimitrova. Reward Interfaces with Best-Effort Implementations. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 30:1-30:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dewes_et_al:LIPIcs.CSL.2026.30,
  author =	{Dewes, Rafael and Dimitrova, Rayna},
  title =	{{Reward Interfaces with Best-Effort Implementations}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{30:1--30:23},
  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.2026.30},
  URN =		{urn:nbn:de:0030-drops-254553},
  doi =		{10.4230/LIPIcs.CSL.2026.30},
  annote =	{Keywords: Component-based design, interface automata, quantitative specifications}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.2
Fine-Grained Complexity of Ontology Mediated Queries (Invited Paper)

Authors: Cristina Feier

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
This article surveys some approaches for establishing fine-grained complexity results for evaluation of ontology mediated queries (OMQs). It accompanies a related talk given at the Reasoning Web Summer School 2024. It zooms into some characterizations of efficiency in a parameterized complexity framework for OMQs based on various description logics and guarded tgds. As such results were established using results from query evaluation on databases, it also discusses the relevant results from the database world. After surveying some successive results on OMQs which all leverage database results in custom ways, it describes an approach which provides a general fpt reduction from query evaluation in the database world to query evaluation in the OMQ world. The reduction enables porting hardness results from the DB world to the OMQ world in a black-box fashion. Along these mentioned approaches, it also provides a brief survey of other approaches which are concerned with fine-grained complexity of OMQs and are based on rewriting techniques.
Cite as

Cristina Feier. Fine-Grained Complexity of Ontology Mediated Queries (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{feier:OASIcs.RW.2024/2025.2,
  author =	{Feier, Cristina},
  title =	{{Fine-Grained Complexity of Ontology Mediated Queries}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{2:1--2:23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.2},
  URN =		{urn:nbn:de:0030-drops-250476},
  doi =		{10.4230/OASIcs.RW.2024/2025.2},
  annote =	{Keywords: complexity analysis, guarded logics, guarded tgds, database theory, ontology mediated queries}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.22
NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks

Authors: Ilan Hartskeerl, Tamara Mchedlidze, Simon van Wageningen, Peter Vangorp, and Alexandru Telea

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
tsNET is a recent graph drawing (GD) method that creates high quality layouts but suffers from a very high runtime. We present a new GD method, NNP-NET, which reduces tsNET’s time complexity to generate layouts for very large graphs in seconds. Additionally, we extend tsNET to support drawing graphs with edge weights. We accomplish this by replacing tsNET’s t-SNE projection with Neural Network Projection (NNP), a fast dimensionality reduction (DR) method that can imitate any given DR method. Our experiments show that NNP-NET gets good quality results when compared to other state-of-the art GD methods while yielding a better computational scalability.
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Ilan Hartskeerl, Tamara Mchedlidze, Simon van Wageningen, Peter Vangorp, and Alexandru Telea. NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hartskeerl_et_al:LIPIcs.GD.2025.22,
  author =	{Hartskeerl, Ilan and Mchedlidze, Tamara and van Wageningen, Simon and Vangorp, Peter and Telea, Alexandru},
  title =	{{NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{22:1--22:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.22},
  URN =		{urn:nbn:de:0030-drops-250087},
  doi =		{10.4230/LIPIcs.GD.2025.22},
  annote =	{Keywords: supervised graph drawing, dimensionality reduction, t-SNE}
}
Document
Graph Drawing Contest Abstract
DOI: 10.4230/LIPIcs.GD.2025.43
Winning the GD Challenge for the 4th Time: Our Approach (Graph Drawing Contest Abstract)

Authors: Julien Bianchetti and Laurent Moalic

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
We present the approach we designed to tackle and win the 2025 Graph Drawing Challenge on minimizing the k-planarity of graphs. Our method employs a multi-stage heuristic centered around two Simulated Annealing (SA) algorithms: the first aims to reduce the total number of crossings, while the second improves the k-value. To obtain a good initial solution, we first applied tools from the OGDF library, which helped reduce crossings. The challenge consisted of nine instances to optimize. Our approach achieved the best results on eight out of nine instances - sharing the top score twice with other teams and ranking first alone in six cases.
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Julien Bianchetti and Laurent Moalic. Winning the GD Challenge for the 4th Time: Our Approach (Graph Drawing Contest Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 43:1-43:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bianchetti_et_al:LIPIcs.GD.2025.43,
  author =	{Bianchetti, Julien and Moalic, Laurent},
  title =	{{Winning the GD Challenge for the 4th Time: Our Approach}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{43:1--43:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.43},
  URN =		{urn:nbn:de:0030-drops-250293},
  doi =		{10.4230/LIPIcs.GD.2025.43},
  annote =	{Keywords: Graph Drawing Contest, simulated annealing, k-planarity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.55
Safe Sequences via Dominators in DAGs for Path-Covering Problems

Authors: Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu

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

Abstract
A path-covering problem on a directed acyclic graph (DAG) requires finding a set of source-to-sink paths that cover all the nodes, all the arcs, or subsets thereof, and additionally they are optimal with respect to some function. In this paper we study safe sequences of nodes or arcs, namely sequences that appear in some path of every path cover of a DAG. We show that safe sequences admit a simple characterization via cutnodes. Moreover, we establish a connection between maximal safe sequences and leaf-to-root paths in the source- and sink-dominator trees of the DAG, which may be of independent interest in the extensive literature on dominators. With dominator trees, safe sequences admit an O(n)-size representation and a linear-time output-sensitive enumeration algorithm running in time O(m + o), where n and m are the number of nodes and arcs, respectively, and o is the total length of the maximal safe sequences. We then apply maximal safe sequences to simplify Integer Linear Programs (ILPs) for two path-covering problems, LeastSquares and MinPathError, which are at the core of RNA transcript assembly problems from bioinformatics. On various datasets, maximal safe sequences can be computed in under 0.1 seconds per graph, on average, and ILP solvers whose search space is reduced in this manner exhibit significant speed-ups. For example on graphs with a large width, average speed-ups are in the range 50-250× for MinPathError and in the range 80-350× for LeastSquares. Optimizing ILPs using safe sequences can thus become a fast building block of practical RNA transcript assembly tools, and more generally, of path-covering problems.
Cite as

Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu. Safe Sequences via Dominators in DAGs for Path-Covering Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sena_et_al:LIPIcs.ESA.2025.55,
  author =	{Sena, Francisco and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Safe Sequences via Dominators in DAGs for Path-Covering Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{55:1--55:17},
  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.2025.55},
  URN =		{urn:nbn:de:0030-drops-245230},
  doi =		{10.4230/LIPIcs.ESA.2025.55},
  annote =	{Keywords: directed acyclic graph, path cover, dominator tree, integer linear programming, least squares, minimum path error}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.56
PLS-Completeness of String Permutations

Authors: Dominik Scheder and Johannes Tantow

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

Abstract
Bitstrings can be permuted via permutations and compared via the lexicographic order. In this paper we study the complexity of finding a minimum of a bitstring via given permutations. As finding a global optimum is known to be NP-complete [László Babai and Eugene M. Luks, 1983], we study the local optima via the class PLS [David S. Johnson et al., 1988] and show hardness for PLS. Additionally, we show that even for one permutation the global optimization problem is NP-complete and give a formula that has these permutation as its symmetries. This answers an open question inspired from Kołodziejczyk and Thapen [Leszek Aleksander Kolodziejczyk and Neil Thapen, 2024] and stated at the SAT and interactions seminar in Dagstuhl.
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Dominik Scheder and Johannes Tantow. PLS-Completeness of String Permutations. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 56:1-56:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{scheder_et_al:LIPIcs.ESA.2025.56,
  author =	{Scheder, Dominik and Tantow, Johannes},
  title =	{{PLS-Completeness of String Permutations}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{56:1--56:14},
  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.2025.56},
  URN =		{urn:nbn:de:0030-drops-245245},
  doi =		{10.4230/LIPIcs.ESA.2025.56},
  annote =	{Keywords: PLS, total search problems, local search, permutation groups, symmetry}
}
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
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.35
Fooling Near-Maximal Decision Trees

Authors: William M. Hoza and Zelin Lv

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
For any constant α > 0, we construct an explicit pseudorandom generator (PRG) that fools n-variate decision trees of size m with error ε and seed length (1 + α) ⋅ log₂ m + O(log(1/ε) + log log n). For context, one can achieve seed length (2 + o(1)) ⋅ log₂ m + O(log(1/ε) + log log n) using well-known constructions and analyses of small-bias distributions, but such a seed length is trivial when m ≥ 2^{n/2}. Our approach is to develop a new variant of the classic concept of almost k-wise independence, which might be of independent interest. We say that a distribution X over {0, 1}ⁿ is k-wise ε-probably uniform if every Boolean function f that depends on only k variables satisfies 𝔼[f(X)] ≥ (1 - ε) ⋅ 𝔼[f]. We show how to sample a k-wise ε-probably uniform distribution using a seed of length (1 + α) ⋅ k + O(log(1/ε) + log log n). Meanwhile, we also show how to construct a set H ⊆ 𝔽₂ⁿ such that every feasible system of k linear equations in n variables over 𝔽₂ has a solution in H. The cardinality of H and the time complexity of enumerating H are at most 2^{k + o(k) + polylog n}, whereas small-bias distributions would give a bound of 2^{2k + O(log(n/k))}. By combining our new constructions with work by Chen and Kabanets (TCS 2016), we obtain nontrivial PRGs and hitting sets for linear-size Boolean circuits. Specifically, we get an explicit PRG with seed length (1 - Ω(1)) ⋅ n that fools circuits of size 2.99 ⋅ n over the U₂ basis, and we get a hitting set with time complexity 2^{(1 - Ω(1)) ⋅ n} for circuits of size 2.49 ⋅ n over the B₂ basis.
Cite as

William M. Hoza and Zelin Lv. Fooling Near-Maximal Decision Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 35:1-35:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hoza_et_al:LIPIcs.APPROX/RANDOM.2025.35,
  author =	{Hoza, William M. and Lv, Zelin},
  title =	{{Fooling Near-Maximal Decision Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{35:1--35:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.35},
  URN =		{urn:nbn:de:0030-drops-244019},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.35},
  annote =	{Keywords: almost k-wise independence, decision trees, pseudorandom generators}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.6
QSETH Strikes Again: Finer Quantum Lower Bounds for Lattice Problem, Strong Simulation, Hitting Set Problem, and More

Authors: Yanlin Chen, Yilei Chen, Rajendra Kumar, Subhasree Patro, and Florian Speelman

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
Despite the wide range of problems for which quantum computers offer a computational advantage over their classical counterparts, there are also many problems for which the best known quantum algorithm provides a speedup that is only quadratic, or even subquadratic. Such a situation could also be desirable if we don't want quantum computers to solve certain problems fast - say problems relevant to post-quantum cryptography. When searching for algorithms and when analyzing the security of cryptographic schemes, we would like to have evidence that these problems are difficult to solve on quantum computers; but how do we assess the exact complexity of these problems? For most problems, there are no known ways to directly prove time lower bounds, however it can still be possible to relate the hardness of disparate problems to show conditional lower bounds. This approach has been popular in the classical community, and is being actively developed for the quantum case [Aaronson et al., 2020; Buhrman et al., 2021; Harry Buhrman et al., 2022; Andris Ambainis et al., 2022]. In this paper, by the use of the QSETH framework [Buhrman et al., 2021] we are able to understand the quantum complexity of a few natural variants of CNFSAT, such as parity-CNFSAT or counting-CNFSAT, and also are able to comment on the non-trivial complexity of approximate versions of counting-CNFSAT. Without considering such variants, the best quantum lower bounds will always be quadratically lower than the equivalent classical bounds, because of Grover’s algorithm; however, we are able to show that quantum algorithms will likely not attain even a quadratic speedup for many problems. These results have implications for the complexity of (variations of) lattice problems, the strong simulation and hitting set problems, and more. In the process, we explore the QSETH framework in greater detail and present a useful guide on how to effectively use the QSETH framework.
Cite as

Yanlin Chen, Yilei Chen, Rajendra Kumar, Subhasree Patro, and Florian Speelman. QSETH Strikes Again: Finer Quantum Lower Bounds for Lattice Problem, Strong Simulation, Hitting Set Problem, and More. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 6:1-6:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2025.6,
  author =	{Chen, Yanlin and Chen, Yilei and Kumar, Rajendra and Patro, Subhasree and Speelman, Florian},
  title =	{{QSETH Strikes Again: Finer Quantum Lower Bounds for Lattice Problem, Strong Simulation, Hitting Set Problem, and More}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{6:1--6:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.6},
  URN =		{urn:nbn:de:0030-drops-243723},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.6},
  annote =	{Keywords: Quantum conditional lower bounds, Fine-grained complexity, Lattice problems, Quantum strong simulation, Hitting set problem, QSETH}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.8
Dynamic Membership for Regular Tree Languages

Authors: Antoine Amarilli, Corentin Barloy, Louis Jachiet, and Charles Paperman

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

Abstract
We study the dynamic membership problem for regular tree languages under relabeling updates: we fix an alphabet Σ and a regular tree language L over Σ (expressed, e.g., as a tree automaton), we are given a tree T with labels in Σ, and we must maintain the information of whether the tree T belongs to L while handling relabeling updates that change the labels of individual nodes in T. Our first contribution is to show that this problem admits an O(log n / log log n) algorithm for any fixed regular tree language, improving over known O(log n) algorithms. This generalizes the known O(log n / log log n) upper bound over words, and it matches the lower bound of Ω(log n / log log n) from dynamic membership to some word languages and from the existential marked ancestor problem. Our second contribution is to introduce a class of regular languages, dubbed almost-commutative tree languages, and show that dynamic membership to such languages under relabeling updates can be decided in constant time per update. Almost-commutative languages generalize both commutative languages and finite languages: they are the analogue for trees of the ZG languages enjoying constant-time dynamic membership over words. Our main technical contribution is to show that this class is conditionally optimal when we assume that the alphabet features a neutral letter, i.e., a letter that has no effect on membership to the language. More precisely, we show that any regular tree language with a neutral letter which is not almost-commutative cannot be maintained in constant time under the assumption that the prefix-U1 problem from [Antoine Amarilli et al., 2021] also does not admit a constant-time algorithm.
Cite as

Antoine Amarilli, Corentin Barloy, Louis Jachiet, and Charles Paperman. Dynamic Membership for Regular Tree Languages. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{amarilli_et_al:LIPIcs.MFCS.2025.8,
  author =	{Amarilli, Antoine and Barloy, Corentin and Jachiet, Louis and Paperman, Charles},
  title =	{{Dynamic Membership for Regular Tree Languages}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{8:1--8:18},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-241155},
  doi =		{10.4230/LIPIcs.MFCS.2025.8},
  annote =	{Keywords: automaton, dynamic membership, incremental maintenance, forest algebra}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.45
Regular Model Checking for Systems with Effectively Regular Reachability Relation

Authors: Javier Esparza and Valentin Krasotin

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

Abstract
Regular model checking is a well-established technique for the verification of regular transition systems (RTS): transition systems whose initial configurations and transition relation can be effectively encoded as regular languages. In 2008, To and Libkin studied RTSs in which the reachability relation (the reflexive and transitive closure of the transition relation) is also effectively regular, and showed that the recurrent reachability problem (whether a regular set L of configurations is reached infinitely often) is polynomial in the size of RTS and the transducer for the reachability relation. We extend the work of To and Libkin by studying the decidability and complexity of verifying almost-sure reachability and recurrent reachability - that is, whether L is reachable or recurrently reachable with probability 1. We then apply our results to the more common case in which only a regular overapproximation of the reachability relation is available. In particular, we extend recent complexity results on verifying safety using regular abstraction frameworks - a technique recently introduced by Czerner, the authors, and Welzel-Mohr - to liveness and almost-sure properties.
Cite as

Javier Esparza and Valentin Krasotin. Regular Model Checking for Systems with Effectively Regular Reachability Relation. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{esparza_et_al:LIPIcs.MFCS.2025.45,
  author =	{Esparza, Javier and Krasotin, Valentin},
  title =	{{Regular Model Checking for Systems with Effectively Regular Reachability Relation}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{45:1--45:19},
  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.2025.45},
  URN =		{urn:nbn:de:0030-drops-241525},
  doi =		{10.4230/LIPIcs.MFCS.2025.45},
  annote =	{Keywords: Regular model checking, abstraction, inductive invariants}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.8
Model Checking as Program Verification by Abstract Interpretation

Authors: Paolo Baldan, Roberto Bruni, Francesco Ranzato, and Diletta Rigo

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
Abstract interpretation offers a powerful toolset for static analysis, tackling precision, complexity and state-explosion issues. In the literature, state partitioning abstractions based on (bi)simulation and property-preserving state relations have been successfully applied to abstract model checking. Here, we pursue a different track in which model checking is seen as an instance of program verification. To this purpose, we introduce a suitable language - called MOKA (for MOdel checking as abstract interpretation of 𝖪leene 𝖠lgebras) - which is used to encode temporal formulae as programs. In particular, we show that (universal fragments of) temporal logics, such as ACTL or, more generally, universal μ-calculus can be transformed into MOKA programs. Such programs return all and only the initial states which violate the formula. By applying abstract interpretation to MOKA programs, we pave the way for reusing more general abstractions than partitions as well as for tuning the precision of the abstraction to remove or avoid false alarms. We show how to perform model checking via a program logic that combines under-approximation and abstract interpretation analysis to avoid false alarms. The notion of locally complete abstraction is used to dynamically improve the analysis precision via counterexample-guided domain refinement.
Cite as

Paolo Baldan, Roberto Bruni, Francesco Ranzato, and Diletta Rigo. Model Checking as Program Verification by Abstract Interpretation. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baldan_et_al:LIPIcs.CONCUR.2025.8,
  author =	{Baldan, Paolo and Bruni, Roberto and Ranzato, Francesco and Rigo, Diletta},
  title =	{{Model Checking as Program Verification by Abstract Interpretation}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.8},
  URN =		{urn:nbn:de:0030-drops-239583},
  doi =		{10.4230/LIPIcs.CONCUR.2025.8},
  annote =	{Keywords: ACTL, \mu-calculus, model checking, abstract interpretation, program analysis, local completeness, abstract interpretation repair, domain refinement, Kleene algebra with tests}
}
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