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DOI: 10.4230/LIPIcs.ITCS.2026.86

The Secretary Problem with Predictions and a Chosen Order

Authors: Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi, Mohammad Hajiesmaili, and Cameron Musco

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

Abstract

We study a learning-augmented variant of the secretary problem, recently introduced by Fujii and Yoshida (2023). In this variant, the decision-maker has access to machine-learned predictions of candidate values in advance. The key challenge is to balance consistency and robustness: when the predictions are accurate, the algorithm should hire a near-best secretary; however, if they are inaccurate, the algorithm should still achieve a bounded competitive ratio. We consider both the standard Random Order Secretary Problem (ROSP), where candidates arrive in a uniform random order, and a more natural model in the learning-augmented setting, where the decision-maker can choose the arrival order based on the predicted candidate values. This model, which we call the Chosen Order Secretary Problem (COSP), can capture scenarios such as an interview schedule that is set by the decision-maker. We propose a novel algorithm that applies to both ROSP and COSP. Building on the approach of Fujii and Yoshida, our method switches from fully trusting predictions to a threshold-based rule when a large deviation of a prediction is observed. Importantly, unlike the algorithm of Fujii and Yoshida, our algorithm uses randomization as part of its decision logic. We show that if ε ∈ [0,1] denotes the maximum multiplicative prediction error, then for ROSP our algorithm achieves competitive ratio max {0.221, (1-ε)/(1+ε)}, improving on a previous bound of max {0.215, (1-ε)/(1+ε)} due to Fujii and Yoshida [Fujii and Yoshida, 2023]. For COSP, our algorithm achieves max {0.262, (1-ε)/(1+ε)}. This surpasses a 0.25 upper bound on the worst-case competitive ratio that applies to the approach of Fujii and Yoshida, and gets closer to the classical secretary benchmark of 1/e ≈ 0.368, which is an upper bound for any algorithm. Our result for COSP highlights the benefit of integrating predictions with arrival-order control in online decision-making.

Cite as

Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi, Mohammad Hajiesmaili, and Cameron Musco. The Secretary Problem with Predictions and a Chosen Order. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 86:1-86:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{karisani_et_al:LIPIcs.ITCS.2026.86,
  author =	{Karisani, Helia and Daneshvaramoli, Mohammadreza and Beyhaghi, Hedyeh and Hajiesmaili, Mohammad and Musco, Cameron},
  title =	{{The Secretary Problem with Predictions and a Chosen Order}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{86:1--86:24},
  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.2026.86},
  URN =		{urn:nbn:de:0030-drops-253734},
  doi =		{10.4230/LIPIcs.ITCS.2026.86},
  annote =	{Keywords: Secretary problem, learning-augmented algorithms, online algorithms}
}

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DOI: 10.4230/LIPIcs.FSTTCS.2025.8

Parameterized Verification of Timed Networks with Clock Invariants

Authors: Étienne André, Swen Jacobs, Shyam Lal Karra, and Ocan Sankur

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract

We consider parameterized verification problems for networks of timed automata (TAs) based on different communication primitives. To this end, we first consider disjunctive timed networks (DTNs), i.e., networks of TAs that communicate via location guards that enable a transition only if there is another process in a certain location. We solve for the first time the case with unrestricted clock invariants, and establish that the parameterized model checking problem (PMCP) over finite local traces can be reduced to the corresponding model checking problem on a single TA. Moreover, we prove that the PMCP for networks that communicate via lossy broadcast can be reduced to the PMCP for DTNs. Finally, we show that for networks with k-wise synchronization, and therefore also for timed Petri nets, location reachability can be reduced to location reachability in DTNs. As a consequence we can answer positively the open problem from Abdulla et al. (2018) whether the universal safety problem for timed Petri nets with multiple clocks is decidable.

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Étienne André, Swen Jacobs, Shyam Lal Karra, and Ocan Sankur. Parameterized Verification of Timed Networks with Clock Invariants. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{andre_et_al:LIPIcs.FSTTCS.2025.8,
  author =	{Andr\'{e}, \'{E}tienne and Jacobs, Swen and Karra, Shyam Lal and Sankur, Ocan},
  title =	{{Parameterized Verification of Timed Networks with Clock Invariants}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.8},
  URN =		{urn:nbn:de:0030-drops-250878},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.8},
  annote =	{Keywords: Networks of Timed Automata, Parameterized Verification, Timed Petri Nets}
}

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DOI: 10.4230/LIPIcs.ESA.2025.52

Beating Competitive Ratio 4 for Graphic Matroid Secretary

Authors: Kiarash Banihashem, MohammadTaghi Hajiaghayi, Dariusz R. Kowalski, Piotr Krysta, Danny Mittal, and Jan Olkowski

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

Abstract

One of the classic problems in online decision-making is the secretary problem, where the goal is to hire the best secretary out of n rankable applicants or, in a natural extension, to maximize the probability of selecting the largest number from a sequence arriving in random order. Many works have considered generalizations of this problem where one can accept multiple values subject to a combinatorial constraint. The seminal work of Babaioff, Immorlica, Kempe, and Kleinberg (SODA'07, JACM'18) proposed the matroid secretary conjecture, suggesting that there exists an O(1)-competitive algorithm for the matroid constraint, and many works since have attempted to obtain algorithms for both general matroids and specific classes of matroids. The ultimate goal of these results is to obtain an e-competitive algorithm, and the strong matroid secretary conjecture states that this is possible for general matroids. One of the most important classes of matroids is the graphic matroid, where a set of edges in a graph is deemed independent if it contains no cycle. Given the rich combinatorial structure of graphs, obtaining algorithms for these matroids is often seen as a good first step towards solving the problem for general matroids. For matroid secretary, Babaioff et al. (SODA'07, JACM'18) first studied graphic matroid case and obtained a 16-competitive algorithm. Subsequent works have improved the competitive ratio, most recently to 4 by Soto, Turkieltaub, and Verdugo (SODA'18). In this paper, we break the 4-competitive barrier for the problem, obtaining a new algorithm with a competitive ratio of 3.95. For the special case of simple graphs (i.e., graphs that do not contain parallel edges) we further improve this to 3.77. Intuitively, solving the problem for simple graphs is easier as they do not contain cycles of length two. A natural question that arises is whether we can obtain a ratio arbitrarily close to e by assuming the graph has a large enough girth. We answer this question affirmatively, proving that one can obtain a competitive ratio arbitrarily close to e even for constant values of girth, providing further evidence for the strong matroid secretary conjecture. We further show that this bound is tight: for any constant g, one cannot obtain a competitive ratio better than e even if we assume that the input graph has girth at least g. To our knowledge, such a bound was not previously known even for simple graphs.

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Kiarash Banihashem, MohammadTaghi Hajiaghayi, Dariusz R. Kowalski, Piotr Krysta, Danny Mittal, and Jan Olkowski. Beating Competitive Ratio 4 for Graphic Matroid Secretary. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 52:1-52:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banihashem_et_al:LIPIcs.ESA.2025.52,
  author =	{Banihashem, Kiarash and Hajiaghayi, MohammadTaghi and Kowalski, Dariusz R. and Krysta, Piotr and Mittal, Danny and Olkowski, Jan},
  title =	{{Beating Competitive Ratio 4 for Graphic Matroid Secretary}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{52:1--52:16},
  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.2025.52},
  URN =		{urn:nbn:de:0030-drops-245205},
  doi =		{10.4230/LIPIcs.ESA.2025.52},
  annote =	{Keywords: online algorithms, graphic matroids, secretary problem}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2025.13

Solving Partial Dominating Set and Related Problems Using Twin-Width

Authors: Jakub Balabán, Daniel Mock, and Peter Rossmanith

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

Abstract

Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are W[1]-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including nowhere-dense classes. In this paper, we demonstrate that these problems are also fixed-parameter tractable with respect to the twin-width of a graph. Indeed, we establish a more general result: every graph property that can be expressed by a logical formula of the form ϕ≡∃ x₁⋯ ∃ x_k ∑_{α ∈ I} #y ψ_α(x₁,…,x_k,y) ≥ t, where ψ_α is a quantifier-free formula for each α ∈ I, t is an arbitrary number, and #y is a counting quantifier, can be evaluated in time f(d,k)n, where n is the number of vertices and d is the width of a contraction sequence that is part of the input. In addition to the aforementioned problems, this includes also connected partial dominating set and independent partial dominating set.

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Jakub Balabán, Daniel Mock, and Peter Rossmanith. Solving Partial Dominating Set and Related Problems Using Twin-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balaban_et_al:LIPIcs.MFCS.2025.13,
  author =	{Balab\'{a}n, Jakub and Mock, Daniel and Rossmanith, Peter},
  title =	{{Solving Partial Dominating Set and Related Problems Using Twin-Width}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{13:1--13:19},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-241203},
  doi =		{10.4230/LIPIcs.MFCS.2025.13},
  annote =	{Keywords: Partial Dominating Set, Partial Vertex Cover, meta-algorithm, counting logic, twin-width}
}

Document

DOI: 10.4230/LIPIcs.WABI.2025.10

DiVerG: Scalable Distance Index for Validation of Paired-End Alignments in Sequence Graphs

Authors: Ali Ghaffaari, Alexander Schönhuth, and Tobias Marschall

Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)

Abstract

Determining the distance between two loci within a genomic region is a recurrent operation in various tasks in computational genomics. A notable example of this task arises in paired-end read mapping as a form of validation of distances between multiple alignments. While straightforward for a single genome, graph-based reference structures render the operation considerably more involved. Given the sheer number of such queries in a typical read mapping experiment, an efficient algorithm for answering distance queries is crucial. In this paper, we introduce DiVerG, a compact data structure as well as a fast and scalable algorithm, for constructing distance indexes for general sequence graphs on multi-core CPU and many-core GPU architectures. DiVerG is based on PairG [Jain et al., 2019], but overcomes the limitations of PairG by exploiting the extensive potential for improvements in terms of scalability and space efficiency. As a consequence, DiVerG can process substantially larger datasets, such as whole human genomes, which are unmanageable by PairG. DiVerG offers faster index construction time and consistently faster query time with gains proportional to the size of the underlying compact data structure. We demonstrate that our method performs favorably on multiple real datasets at various scales. DiVerG achieves superior performance over PairG; e.g. resulting to 2.5-4x speed-up in query time, 44-340x smaller index size, and 3-50x faster construction time for the genome graph of the MHC region, as a particularly variable region of the human genome. The implementation is available at: https://github.com/cartoonist/diverg

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Ali Ghaffaari, Alexander Schönhuth, and Tobias Marschall. DiVerG: Scalable Distance Index for Validation of Paired-End Alignments in Sequence Graphs. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 10:1-10:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghaffaari_et_al:LIPIcs.WABI.2025.10,
  author =	{Ghaffaari, Ali and Sch\"{o}nhuth, Alexander and Marschall, Tobias},
  title =	{{DiVerG: Scalable Distance Index for Validation of Paired-End Alignments in Sequence Graphs}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{10:1--10:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.10},
  URN =		{urn:nbn:de:0030-drops-239369},
  doi =		{10.4230/LIPIcs.WABI.2025.10},
  annote =	{Keywords: Sequence graph, distance index, read mapping, sparse matrix}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.18

q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations

Authors: Kiril Bangachev and S. Matthew Weinberg

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

Abstract

For a set M of m elements, we define a decreasing chain of classes of normalized monotone-increasing valuation functions from 2^M to ℝ_{≥ 0}, parameterized by an integer q ∈ [2,m]. For a given q, we refer to the class as q-partitioning. A valuation function is subadditive if and only if it is 2-partitioning, and fractionally subadditive if and only if it is m-partitioning. Thus, our chain establishes an interpolation between subadditive and fractionally subadditive valuations. We show that this interpolation is smooth (q-partitioning valuations are "nearly" (q-1)-partitioning in a precise sense, Theorem 6), interpretable (the definition arises by analyzing the core of a cost-sharing game, à la the Bondareva-Shapley Theorem for fractionally subadditive valuations, Section 3.1), and non-trivial (the class of q-partitioning valuations is distinct for all q, Proposition 3). For domains where provable separations exist between subadditive and fractionally subadditive, we interpolate the stronger guarantees achievable for fractionally subadditive valuations to all q ∈ {2,…, m}. Two highlights are the following: 1) An Ω ((log log q)/(log log m))-competitive posted price mechanism for q-partitioning valuations. Note that this matches asymptotically the state-of-the-art for both subadditive (q = 2) [Paul Dütting et al., 2020], and fractionally subadditive (q = m) [Feldman et al., 2015]. 2) Two upper-tail concentration inequalities on 1-Lipschitz, q-partitioning valuations over independent items. One extends the state-of-the-art for q = m to q < m, the other improves the state-of-the-art for q = 2 for q > 2. Our concentration inequalities imply several corollaries that interpolate between subadditive and fractionally subadditive, for example: 𝔼[v(S)] ≤ (1 + 1/log q)Median[v(S)] + O(log q). To prove this, we develop a new isoperimetric inequality using Talagrand’s method of control by q points, which may be of independent interest. We also discuss other probabilistic inequalities and game-theoretic applications of q-partitioning valuations, and connections to subadditive MPH-k valuations [Tomer Ezra et al., 2019].

Cite as

Kiril Bangachev and S. Matthew Weinberg. q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bangachev_et_al:LIPIcs.ICALP.2025.18,
  author =	{Bangachev, Kiril and Weinberg, S. Matthew},
  title =	{{q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{18:1--18:20},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-233956},
  doi =		{10.4230/LIPIcs.ICALP.2025.18},
  annote =	{Keywords: Subadditive Functions, Fractionally Subadditive Functions, Posted Price Mechanisms, Concentration Inequalities}
}

@InProceedings{bangachev_et_al:LIPIcs.ICALP.2025.18,
  author =	{Bangachev, Kiril and Weinberg, S. Matthew},
  title =	{{q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{18:1--18:20},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-233956},
  doi =		{10.4230/LIPIcs.ICALP.2025.18},
  annote =	{Keywords: Subadditive Functions, Fractionally Subadditive Functions, Posted Price Mechanisms, Concentration Inequalities}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.137

Universal Online Contention Resolution with Preselected Order

Authors: Junyao Zhao

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

Abstract

Online contention resolution scheme (OCRS) is a powerful technique for online decision making, which - in the case of matroids - given a matroid and a prior distribution of active elements, selects a subset of active elements that satisfies the matroid constraint in an online fashion. OCRS has been studied mostly for product distributions in the literature. Recently, universal OCRS, that works even for correlated distributions, has gained interest, because it naturally generalizes the classic notion, and its existence in the random-order arrival model turns out to be equivalent to the matroid secretary conjecture. However, currently very little is known about how to design universal OCRSs for any arrival model. In this work, we consider a natural and relatively flexible arrival model, where the OCRS is allowed to preselect (i.e., non-adaptively select) the arrival order of the elements, and within this model, we design simple and optimal universal OCRSs that are computationally efficient. In the course of deriving our OCRSs, we also discover an efficient reduction from universal online contention resolution to the matroid secretary problem for any arrival model, answering a question posed in [Dughmi, 2020].

Cite as

Junyao Zhao. Universal Online Contention Resolution with Preselected Order. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 137:1-137:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhao:LIPIcs.ICALP.2025.137,
  author =	{Zhao, Junyao},
  title =	{{Universal Online Contention Resolution with Preselected Order}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{137:1--137:17},
  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.2025.137},
  URN =		{urn:nbn:de:0030-drops-235147},
  doi =		{10.4230/LIPIcs.ICALP.2025.137},
  annote =	{Keywords: Matroids, online contention resolution schemes, secretary problems}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.4

A Bicriterion Concentration Inequality and Prophet Inequalities for k-Fold Matroid Unions

Authors: Noga Alon, Nick Gravin, Tristan Pollner, Aviad Rubinstein, Hongao Wang, S. Matthew Weinberg, and Qianfan Zhang

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

We investigate prophet inequalities with competitive ratios approaching 1, seeking to generalize k-uniform matroids. We first show that large girth does not suffice: for all k, there exists a matroid of girth ≥ k and a prophet inequality instance on that matroid whose optimal competitive ratio is 1/2. Next, we show k-fold matroid unions do suffice: we provide a prophet inequality with competitive ratio 1-O(√{(log k)/k}) for any k-fold matroid union. Our prophet inequality follows from an online contention resolution scheme. The key technical ingredient in our online contention resolution scheme is a novel bicriterion concentration inequality for arbitrary monotone 1-Lipschitz functions over independent items which may be of independent interest. Applied to our particular setting, our bicriterion concentration inequality yields "Chernoff-strength" concentration for a 1-Lipschitz function that is not (approximately) self-bounding.

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Noga Alon, Nick Gravin, Tristan Pollner, Aviad Rubinstein, Hongao Wang, S. Matthew Weinberg, and Qianfan Zhang. A Bicriterion Concentration Inequality and Prophet Inequalities for k-Fold Matroid Unions. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alon_et_al:LIPIcs.ITCS.2025.4,
  author =	{Alon, Noga and Gravin, Nick and Pollner, Tristan and Rubinstein, Aviad and Wang, Hongao and Weinberg, S. Matthew and Zhang, Qianfan},
  title =	{{A Bicriterion Concentration Inequality and Prophet Inequalities for k-Fold Matroid Unions}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.4},
  URN =		{urn:nbn:de:0030-drops-226329},
  doi =		{10.4230/LIPIcs.ITCS.2025.4},
  annote =	{Keywords: Prophet Inequalities, Online Contention Resolution Schemes, Concentration Inequalities}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.10

Algorithmic Collusion Without Threats

Authors: Eshwar Ram Arunachaleswaran, Natalie Collina, Sampath Kannan, Aaron Roth, and Juba Ziani

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

There has been substantial recent concern that automated pricing algorithms might learn to "collude." Supra-competitive prices can emerge as a Nash equilibrium of repeated pricing games, in which sellers play strategies which threaten to punish their competitors if they ever "defect" from a set of supra-competitive prices, and these strategies can be automatically learned. But threats are anti-competitive on their face. In fact, a standard economic intuition is that supra-competitive prices emerge from either the use of threats, or a failure of one party to correctly optimize their payoff. Is this intuition correct? Would explicitly preventing threats in algorithmic decision-making prevent supra-competitive prices when sellers are optimizing for their own revenue? No. We show that supra-competitive prices can robustly emerge even when both players are using algorithms which do not explicitly encode threats, and which optimize for their own revenue. Since deploying an algorithm is a form of commitment, we study sequential Bertrand pricing games (and a continuous variant) in which a first mover deploys an algorithm and then a second mover optimizes within the resulting environment. We show that if the first mover deploys any algorithm with a no-regret guarantee, and then the second mover even approximately optimizes within this now static environment, monopoly-like prices arise. The result holds for any no-regret learning algorithm deployed by the first mover and for any pricing policy of the second mover that obtains them profit at least as high as a random pricing would - and hence the result applies even when the second mover is optimizing only within a space of non-responsive pricing distributions which are incapable of encoding threats. In fact, there exists a set of strategies, neither of which explicitly encode threats that form a Nash equilibrium of the simultaneous pricing game in algorithm space, and lead to near monopoly prices. This suggests that the definition of "algorithmic collusion" may need to be expanded, to include strategies without explicitly encoded threats.

Cite as

Eshwar Ram Arunachaleswaran, Natalie Collina, Sampath Kannan, Aaron Roth, and Juba Ziani. Algorithmic Collusion Without Threats. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{arunachaleswaran_et_al:LIPIcs.ITCS.2025.10,
  author =	{Arunachaleswaran, Eshwar Ram and Collina, Natalie and Kannan, Sampath and Roth, Aaron and Ziani, Juba},
  title =	{{Algorithmic Collusion Without Threats}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.10},
  URN =		{urn:nbn:de:0030-drops-226386},
  doi =		{10.4230/LIPIcs.ITCS.2025.10},
  annote =	{Keywords: Algorithmic Game Theory, Algorithmic Collusion, No-Regret Dynamics}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.52

Combinatorial Pen Testing (Or Consumer Surplus of Deferred-Acceptance Auctions)

Authors: Aadityan Ganesh and Jason Hartline

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

Pen testing is the problem of selecting high-capacity resources when the only way to measure the capacity of a resource expends its capacity. We have a set of n pens with unknown amounts of ink and our goal is to select a feasible subset of pens maximizing the total ink in them. We are allowed to learn about the ink levels by writing with them, but this uses up ink that was previously in the pens. We identify optimal and near optimal pen testing algorithms by drawing analogues to auction theoretic frameworks of deferred-acceptance auctions and virtual values. Our framework allows the conversion of any near optimal deferred-acceptance mechanism into a near optimal pen testing algorithm. Moreover, these algorithms guarantee an additional overhead of at most (1+o(1)) ln n in the approximation factor to the omniscient algorithm that has access to the ink levels in the pens. We use this framework to give pen testing algorithms for various combinatorial constraints like matroid, knapsack, and general downward-closed constraints, and also for online environments.

Cite as

Aadityan Ganesh and Jason Hartline. Combinatorial Pen Testing (Or Consumer Surplus of Deferred-Acceptance Auctions). In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 52:1-52:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ganesh_et_al:LIPIcs.ITCS.2025.52,
  author =	{Ganesh, Aadityan and Hartline, Jason},
  title =	{{Combinatorial Pen Testing (Or Consumer Surplus of Deferred-Acceptance Auctions)}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{52:1--52:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.52},
  URN =		{urn:nbn:de:0030-drops-226808},
  doi =		{10.4230/LIPIcs.ITCS.2025.52},
  annote =	{Keywords: Pen testing, consumer surplus, money-burning, deferred-acceptance auctions}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2024.34

On Continuous Pushdown VASS in One Dimension

Authors: Guillermo A. Pérez and Shrisha Rao

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract

A pushdown vector addition system with states (PVASS) extends the model of vector addition systems with a pushdown stack. The algorithmic analysis of PVASS has applications such as static analysis of recursive programs manipulating integer variables. Unfortunately, reachability analysis, even for one-dimensional PVASS is not known to be decidable. So, we relax the model of one-dimensional PVASS to make the counter updates continuous and show that in this case reachability, coverability, and boundedness are decidable in polynomial time. In addition, for the extension of the model with lower-bound guards on the states, we show that coverability and reachability are NP-complete, and boundedness is coNP-complete.

Cite as

Guillermo A. Pérez and Shrisha Rao. On Continuous Pushdown VASS in One Dimension. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{perez_et_al:LIPIcs.CONCUR.2024.34,
  author =	{P\'{e}rez, Guillermo A. and Rao, Shrisha},
  title =	{{On Continuous Pushdown VASS in One Dimension}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{34:1--34:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.34},
  URN =		{urn:nbn:de:0030-drops-208065},
  doi =		{10.4230/LIPIcs.CONCUR.2024.34},
  annote =	{Keywords: Vector addition systems, Pushdown automata, Reachability}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.MFCS.2024.5

Fine-Grained Complexity of Program Analysis (Invited Talk)

Authors: Rupak Majumdar

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract

There is a well-known "cubic bottleneck" in program analysis and language theory: many program analysis problems can be solved in time cubic in the size of the input but, despite years of effort, there are no known sub-cubic algorithms. For example, context-free reachability (whether there is a path in a labeled graph that is labeled with a word from a context-free language), the emptiness problem for pushdown automata, and the recognition problem for two-way nondeterministic pushdown automata all belong to the cubic class. We survey the status of these problems through the lens of fine-grained complexity. We study the related certification task: given an instance of any of these problems, are there small and efficiently checkable certificates for the existence and for the non-existence of a path? We show that, in both scenarios, there exist succinct certificates (O(n²) in the size of the problem) and these certificates can be checked in subcubic (matrix multiplication) time. Thus, all these problems lie in nondeterministic and co-nondeterministic subcubic time. We also study a hierarchy of program analysis problems above the cubic bottleneck. A representative problem here is the recognition problem for two-way nondeterministic pushdown automata with k heads. We show fine-grained hardness results for this hierarchy. We also discuss purely language-theoretic consequences of these results: for example, we obtain hardest languages accepted by two-way nondeterministic multihead pushdown automata, as well as separations between language classes. (Joint work with A. R. Balasubramanian, Dmitry Chistikov, and Philipp Schepper.)

Cite as

Rupak Majumdar. Fine-Grained Complexity of Program Analysis (Invited Talk). In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, p. 5:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{majumdar:LIPIcs.MFCS.2024.5,
  author =	{Majumdar, Rupak},
  title =	{{Fine-Grained Complexity of Program Analysis}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{5:1--5:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.5},
  URN =		{urn:nbn:de:0030-drops-205619},
  doi =		{10.4230/LIPIcs.MFCS.2024.5},
  annote =	{Keywords: Fine-grained complexity, CFL reachability, 2NPDA recognition, PDA emptiness}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2022.17

Complexity of Coverability in Depth-Bounded Processes

Authors: A. R. Balasubramanian

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract

We consider the class of depth-bounded processes in π-calculus. These processes are the most expressive fragment of π-calculus, for which verification problems are known to be decidable. The decidability of the coverability problem for this class has been achieved by means of well-quasi orders. (Meyer, IFIP TCS 2008; Wies, Zufferey and Henzinger, FoSSaCS 2010). However, the precise complexity of this problem has not been known so far, with only a known EXPSPACE-lower bound. In this paper, we prove that coverability for depth-bounded processes is 𝐅_ε₀-complete, where 𝐅_ε₀ is a class in the fast-growing hierarchy of complexity classes. This solves an open problem mentioned by Haase, Schmitz, and Schnoebelen (LMCS, Vol 10, Issue 4) and also addresses a question raised by Wies, Zufferey and Henzinger (FoSSaCS 2010).

Cite as

A. R. Balasubramanian. Complexity of Coverability in Depth-Bounded Processes. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{balasubramanian:LIPIcs.CONCUR.2022.17,
  author =	{Balasubramanian, A. R.},
  title =	{{Complexity of Coverability in Depth-Bounded Processes}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{17:1--17:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.17},
  URN =		{urn:nbn:de:0030-drops-170809},
  doi =		{10.4230/LIPIcs.CONCUR.2022.17},
  annote =	{Keywords: \pi-calculus, Depth-bounded processes, Fast-growing complexity classes}
}

Document

DOI: 10.4230/LIPIcs.FSTTCS.2021.35

Complexity of Coverability in Bounded Path Broadcast Networks

Authors: A. R. Balasubramanian

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract

Broadcast networks are a formalism of distributed computation that allow one to model networks of identical nodes communicating through message broadcasts over a communication topology that does not change over the course of executions. The parameterized verification problem for these networks amounts to proving correctness of a property for any number of nodes, and on all executions. Dually speaking, this problem asks for the existence of an execution of the broadcast network that violates a given property. One specific instance of parameterized verification is the coverability problem which asks whether there is an execution of the network in which some node reaches a given state of the broadcast protocol. This problem was proven to be undecidable by Delzanno, Sangnier and Zavattaro (CONCUR 2010). In the same paper, the authors also prove that, if we additionally assume that the underlying communication topology has a bound on the longest path, then the coverability problem becomes decidable. In this paper, we provide complexity results for the above problem and prove that the coverability problem for bounded-path topologies is 𝐅_ε₀-complete, where 𝐅_ε₀ is a class in the fast-growing hierarchy of complexity classes. This solves an open problem of Hasse, Schmitz and Schnoebelen (LMCS, Vol 10, Issue 4).

Cite as

A. R. Balasubramanian. Complexity of Coverability in Bounded Path Broadcast Networks. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balasubramanian:LIPIcs.FSTTCS.2021.35,
  author =	{Balasubramanian, A. R.},
  title =	{{Complexity of Coverability in Bounded Path Broadcast Networks}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{35:1--35:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.35},
  URN =		{urn:nbn:de:0030-drops-155466},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.35},
  annote =	{Keywords: Parameterized verification, Bounded path networks, Fast-growing complexity classes}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2021.17

Adaptive Synchronisation of Pushdown Automata

Authors: A. R. Balasubramanian and K. S. Thejaswini

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract

We introduce the notion of adaptive synchronisation for pushdown automata, in which there is an external observer who has no knowledge about the current state of the pushdown automaton, but can observe the contents of the stack. The observer would then like to decide if it is possible to bring the automaton from any state into some predetermined state by giving inputs to it in an adaptive manner, i.e., the next input letter to be given can depend on how the contents of the stack changed after the current input letter. We show that for non-deterministic pushdown automata, this problem is 2-EXPTIME-complete and for deterministic pushdown automata, we show EXPTIME-completeness. To prove the lower bounds, we first introduce (different variants of) subset-synchronisation and show that these problems are polynomial-time equivalent with the adaptive synchronisation problem. We then prove hardness results for the subset-synchronisation problems. For proving the upper bounds, we consider the problem of deciding if a given alternating pushdown system has an accepting run with at most k leaves and we provide an n^O(k²) time algorithm for this problem.

Cite as

A. R. Balasubramanian and K. S. Thejaswini. Adaptive Synchronisation of Pushdown Automata. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balasubramanian_et_al:LIPIcs.CONCUR.2021.17,
  author =	{Balasubramanian, A. R. and Thejaswini, K. S.},
  title =	{{Adaptive Synchronisation of Pushdown Automata}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.17},
  URN =		{urn:nbn:de:0030-drops-143948},
  doi =		{10.4230/LIPIcs.CONCUR.2021.17},
  annote =	{Keywords: Adaptive synchronisation, Pushdown automata, Alternating pushdown systems}
}

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