18 Search Results for "Hubáček, Pavel"

Document
DOI: 10.4230/LIPIcs.FUN.2026.19
Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level

Authors: Bernd Gärtner, Sebastian Haslebacher, and Hung P. Hoang

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
ARRIVAL is the problem of deciding whether a token, following a deterministic process, eventually reaches a designated destination. While the problem is known to lie in NP ∩ CoNP, whether it can be solved in polynomial time remains a major open question. In this article, we study ladders, a class of graphs that constitutes a family of worst-case instances for many existing algorithms, including the currently best known algorithm by Gärtner, Haslebacher, and Hoang (ICALP 2021). We show that ARRIVAL restricted to ladders can be solved in polynomial time, and we further extend this result to stopping binary simple stochastic games (SSG).
Cite as

Bernd Gärtner, Sebastian Haslebacher, and Hung P. Hoang. Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gartner_et_al:LIPIcs.FUN.2026.19,
  author =	{G\"{a}rtner, Bernd and Haslebacher, Sebastian and Hoang, Hung P.},
  title =	{{Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.19},
  URN =		{urn:nbn:de:0030-drops-257385},
  doi =		{10.4230/LIPIcs.FUN.2026.19},
  annote =	{Keywords: ARRIVAL, Rotor-Routing, Simple Stochastic Games}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.60
Total Search Problems in ZPP

Authors: Noah Fleming, Stefan Grosser, Siddhartha Jain, Jiawei Li, Hanlin Ren, Morgan Shirley, and Weiqiang Yuan

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

Abstract
We initiate a systematic study of TFZPP, the class of total NP search problems solvable by polynomial time randomized algorithms. TFZPP contains a variety of important search problems such as Bertrand-Chebyshev (finding a prime between N and 2N), refuter problems for many circuit lower bounds, and Lossy-Code. The Lossy-Code problem has found prominence due to its fundamental connections to derandomization, catalytic computing, and the metamathematics of complexity theory, among other areas. While TFZPP collapses to FP under standard derandomization assumptions in the white-box setting, we are able to separate TFZPP from the major TFNP subclasses in the black-box setting. In fact, we are able to separate it from every uniform TFNP class assuming that NP is not in quasi-polynomial time. To do so, we extend the connection between proof complexity and black-box TFNP to randomized proof systems and randomized reductions. Next, we turn to developing a taxonomy of TFZPP problems. We highlight a problem called Nephew, originating from an infinity axiom in set theory. We show that Nephew is in PWPP∩ TFZPP and conjecture that it is not reducible to Lossy-Code. Intriguingly, except for some artificial examples, most other black-box TFZPP problems that we are aware of reduce to Lossy-Code: - We define a problem called Empty-Child capturing finding a leaf in a rooted (binary) tree, and show that this problem is equivalent to Lossy-Code. We also show that a variant of Empty-Child with "heights" is complete for the intersection of SOPL and Lossy-Code. - We strengthen Lossy-Code with several combinatorial inequalities such as the AM-GM inequality. Somewhat surprisingly, we show the resulting new problems are still reducible to Lossy-Code. A technical highlight of this result is that they are proved by formalizations in bounded arithmetic, specifically in Jeřábek’s theory APC₁ (JSL 2007). - Finally, we show that the Dense-Linear-Ordering problem reduces to Lossy-Code.
Cite as

Noah Fleming, Stefan Grosser, Siddhartha Jain, Jiawei Li, Hanlin Ren, Morgan Shirley, and Weiqiang Yuan. Total Search Problems in ZPP. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 60:1-60:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fleming_et_al:LIPIcs.ITCS.2026.60,
  author =	{Fleming, Noah and Grosser, Stefan and Jain, Siddhartha and Li, Jiawei and Ren, Hanlin and Shirley, Morgan and Yuan, Weiqiang},
  title =	{{Total Search Problems in ZPP}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{60:1--60:26},
  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.2026.60},
  URN =		{urn:nbn:de:0030-drops-253473},
  doi =		{10.4230/LIPIcs.ITCS.2026.60},
  annote =	{Keywords: TFNP, lossy code, randomized proof systems, query complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.69
Computing Equilibrium Points of Electrostatic Potentials

Authors: Abheek Ghosh, Paul W. Goldberg, and Alexandros Hollender

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

Abstract
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which solutions are guaranteed to exist due to a nonconstructive argument, but gradient descent is unreliable due to the presence of singularities. We present an algorithm based on piecewise approximation of the potential function by Taylor series. The main insight is to divide the domain into a grid with variable coarseness, where grid cells are exponentially smaller in regions where the function changes rapidly compared to regions where it changes slowly. Our algorithm finds approximate equilibrium points in time poly-logarithmic in the approximation parameter, but these points are not guaranteed to be close to exact solutions. Nevertheless, we show that such points can be computed efficiently under a mild assumption that we call "strong non-degeneracy". We complement these algorithmic results by studying a generalization of this problem and showing that it is CLS-hard and in PPAD, leaving its precise classification as an intriguing open problem.
Cite as

Abheek Ghosh, Paul W. Goldberg, and Alexandros Hollender. Computing Equilibrium Points of Electrostatic Potentials. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 69:1-69:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghosh_et_al:LIPIcs.ITCS.2026.69,
  author =	{Ghosh, Abheek and Goldberg, Paul W. and Hollender, Alexandros},
  title =	{{Computing Equilibrium Points of Electrostatic Potentials}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{69:1--69:22},
  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.2026.69},
  URN =		{urn:nbn:de:0030-drops-253566},
  doi =		{10.4230/LIPIcs.ITCS.2026.69},
  annote =	{Keywords: Total search problems, TFNP, PPAD, CLS, polynomial equations}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.8
Intersection Theorems: A Potential Approach to Proof Complexity Lower Bounds

Authors: Yaroslav Alekseev and Nikita Gaevoy

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

Abstract
Recently, Göös et al. [Göös et al., 2024] showed that Res ⋏ uSA = RevRes in the following sense: if a formula φ has refutations of size at most s and width/degree at most w in both Res and uSA, then there is a refutation for φ of size at most poly(s ⋅ 2^w) in RevRes. Their proof relies on the TFNP characterization of the aforementioned proof systems. In our work, we give a direct and simplified proof of this result, simultaneously achieving better bounds: we show that if for a formula φ there are refutations of size at most s in both Res and uSA, then there is a refutation of φ of size at most poly(s) in RevRes. This potentially allows us to "lift" size lower bounds from RevRes to Res for the formulas for which there are upper bounds in uSA. This kind of lifting was not possible before because of the exponential blow-up in size from the width. Similarly, we improve the bounds in another intersection theorem from [Göös et al., 2024] by giving a direct proof of Res ⋏ uNS = RevResT. Finally, we generalize those intersection theorems to some proof systems for which we currently do not have a TFNP characterization. For example, we show that Res(⊕) ⋏ u-wRes(⊕) = RevRes(⊕), which effectively allows us to reduce the problem of proving Pigeonhole Principle lower bounds in Res(⊕) to proving Pigeonhole Principle lower bounds in RevRes(⊕), a potentially weaker proof system.
Cite as

Yaroslav Alekseev and Nikita Gaevoy. Intersection Theorems: A Potential Approach to Proof Complexity Lower Bounds. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alekseev_et_al:LIPIcs.ITCS.2026.8,
  author =	{Alekseev, Yaroslav and Gaevoy, Nikita},
  title =	{{Intersection Theorems: A Potential Approach to Proof Complexity Lower Bounds}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{8:1--8:18},
  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.2026.8},
  URN =		{urn:nbn:de:0030-drops-252953},
  doi =		{10.4230/LIPIcs.ITCS.2026.8},
  annote =	{Keywords: proof complexity, intersection theorems}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.6
Foundations of Fiat-Denominated Loans Collateralized by Cryptocurrencies

Authors: Pavel Hubáček, Jan Václavek, and Michelle Yeo

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
The rising importance of cryptocurrencies as financial assets pushed their applicability from an object of speculation closer to standard financial instruments such as loans. In this work, we initiate the study of secure protocols that enable fiat-denominated loans collateralized by cryptocurrencies such as Bitcoin. We provide limited-custodial protocols for such loans relying only on trusted arbitration and provide their game-theoretical analysis. We also highlight various interesting directions for future research.
Cite as

Pavel Hubáček, Jan Václavek, and Michelle Yeo. Foundations of Fiat-Denominated Loans Collateralized by Cryptocurrencies. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hubacek_et_al:LIPIcs.OPODIS.2025.6,
  author =	{Hub\'{a}\v{c}ek, Pavel and V\'{a}clavek, Jan and Yeo, Michelle},
  title =	{{Foundations of Fiat-Denominated Loans Collateralized by Cryptocurrencies}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.6},
  URN =		{urn:nbn:de:0030-drops-251796},
  doi =		{10.4230/LIPIcs.OPODIS.2025.6},
  annote =	{Keywords: Blockchains, Cryptocurrencies, DeFi, Loans, Mechanism design, Subgame Perfect Equilibrium, Rational analysis}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.19
Two-Tier Black-Box Blockchains and Application to Instant Layer-1 Payments

Authors: Michele Ciampi, Yun Lu, Rafail Ostrovsky, and Vassilis Zikas

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

Abstract
Common blockchain protocols are monolithic, i.e., their security relies on a single assumption, e.g., honest majority of hashing power (Bitcoin) or stake (Cardano, Algorand, Ethereum). In contrast, so-called optimistic approaches (Thunderella, Meshcash) rely on a combination of assumptions to achieve faster transaction liveness. We revisit, redesign, and augment the optimistic paradigm to a tiered approach. Our design assumes a primary (Tier 1) and a secondary (Tier 2, also referred to as fallback) blockchain, and achieves full security also in a tiered fashion: If the assumption underpinning the primary chain holds, then we guarantee safety, liveness and censorship resistance, irrespectively of the status of the fallback chain. And even if the primary assumption fails, all security properties are still satisfied (albeit with a temporary slow down) provided the fallback assumption holds. To our knowledge, no existing optimistic or tiered approach preserves both safety and liveness when any one of its underlying blockchain (assumptions) fails. The above is achieved by a new detection-and-recovery mechanism that links the two blockchains, so that any violation of safety, liveness, or censorship resistance on the (faster) primary blockchain is temporary - it is swiftly detected and recovered on the secondary chain - and thus cannot result in a persistent fork or halt of the blockchain ledger. We instantiate the above paradigm using a primary chain based on proof of reputation (PoR) and a fallback chain based on proof of stake (PoS). Our construction uses the PoR and PoS blockchains in a mostly black-box manner - where rather than assuming a concrete construction we distil abstract properties on the two blockchains that are sufficient for applying our tiered methodology. In fact, choosing reputation as the resource of the primary chain opens the door to an incentive mechanism - which we devise and analyze - that tokenizes reputation in order to deter cheating and boost participation (on both the primary/PoR and the fallback/PoS blockchain). As we demonstrate, such tokenization in combination with interpreting reputation as a built-in system-wide credit score, allows for embedding in our two-tiered methodology a novel mechanism which provides collateral-free, multi-use payment-channel-like functionality where payments can be instantly confirmed.
Cite as

Michele Ciampi, Yun Lu, Rafail Ostrovsky, and Vassilis Zikas. Two-Tier Black-Box Blockchains and Application to Instant Layer-1 Payments. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ciampi_et_al:LIPIcs.AFT.2025.19,
  author =	{Ciampi, Michele and Lu, Yun and Ostrovsky, Rafail and Zikas, Vassilis},
  title =	{{Two-Tier Black-Box Blockchains and Application to Instant Layer-1 Payments}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{19:1--19:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.19},
  URN =		{urn:nbn:de:0030-drops-247380},
  doi =		{10.4230/LIPIcs.AFT.2025.19},
  annote =	{Keywords: Fault tolerant blockchain, instantly confirmed payments}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.50
Shared Randomness in Locally Checkable Problems: The Role of Computational Assumptions

Authors: Adar Hadad and Moni Naor

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

Abstract
Shared randomness is a valuable resource in distributed computing, allowing some form of coordination between processors without explicit communication. But what happens when the shared random string can affect the inputs to the system? Consider the class of distributed graph problems where the correctness of solutions can be checked locally, known as Locally Checkable Labelings (LCL). LCL problems have been extensively studied in the LOCAL model, where nodes operate in synchronous rounds and have access only to local information. This has led to intriguing insights regarding the power of private randomness. E.g., for certain round complexity classes, derandomization does not incur an overhead (asymptotically). This work considers a setting where the randomness is public. Recently, an LCL problem for which shared randomness can reduce the round complexity was discovered by Balliu et al. (ICALP 2025). This result applies to inputs set obliviously of the shared randomness, which may not always be a plausible assumption. We define a model where the inputs can be adversarially chosen, even based on the shared randomness, which we now call preset public coins. We study LCL problems in the preset public coins model, under assumptions regarding the computational power of the adversary that selects the input. We show connections to hardness in the class TFNP. Our results are: 1) Assuming a hard-on-average problem in TFNP, we present an LCL problem that, in the preset public coins model, demonstrates a gap in the round complexity between polynomial-time and unbounded adversaries. 2) An LCL problem for which the error probability is significantly higher when facing unbounded adversaries implies a hard-on-average problem in TFNP/poly.
Cite as

Adar Hadad and Moni Naor. Shared Randomness in Locally Checkable Problems: The Role of Computational Assumptions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 50:1-50:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hadad_et_al:LIPIcs.APPROX/RANDOM.2025.50,
  author =	{Hadad, Adar and Naor, Moni},
  title =	{{Shared Randomness in Locally Checkable Problems: The Role of Computational Assumptions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{50:1--50:23},
  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.2025.50},
  URN =		{urn:nbn:de:0030-drops-244161},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.50},
  annote =	{Keywords: Distributed Graph Algorithms, Common Random String, Cryptographic Hardness}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.95
ARRIVAL: Recursive Framework & 𝓁₁-Contraction

Authors: Sebastian Haslebacher

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

Abstract
ARRIVAL is the problem of deciding which out of two possible destinations will be reached first by a token that moves deterministically along the edges of a directed graph, according to so-called switching rules. It is known to lie in NP ∩ CoNP, but not known to lie in 𝖯. The state-of-the-art algorithm due to Gärtner et al. (ICALP `21) runs in time 2^{𝒪(√n log n)} on an n-vertex graph. We prove that ARRIVAL can be solved in time 2^{𝒪(k log² n)} on n-vertex graphs of treewidth k. Our algorithm is derived by adapting a simple recursive algorithm for a generalization of ARRIVAL called G-ARRIVAL. This simple recursive algorithm acts as a framework from which we can also rederive the subexponential upper bound of Gärtner et al. Our second result is a reduction from G-ARRIVAL to the problem of finding an approximate fixed point of an 𝓁₁-contracting function f : [0, 1]ⁿ → [0, 1]ⁿ. Finding such fixed points is a well-studied problem in the case of the 𝓁₂-metric and the 𝓁_∞-metric, but little is known about the 𝓁₁-case. Both of our results highlight parallels between ARRIVAL and the Simple Stochastic Games (SSG) problem. Concretely, Chatterjee et al. (SODA `23) gave an algorithm for SSG parameterized by treewidth that achieves a similar bound as we do for ARRIVAL, and SSG is known to reduce to 𝓁_∞-contraction.
Cite as

Sebastian Haslebacher. ARRIVAL: Recursive Framework & 𝓁₁-Contraction. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 95:1-95:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haslebacher:LIPIcs.ICALP.2025.95,
  author =	{Haslebacher, Sebastian},
  title =	{{ARRIVAL: Recursive Framework \& 𝓁₁-Contraction}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{95:1--95:17},
  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.2025.95},
  URN =		{urn:nbn:de:0030-drops-234723},
  doi =		{10.4230/LIPIcs.ICALP.2025.95},
  annote =	{Keywords: ARRIVAL, G-ARRIVAL, Deterministic Random Walk, Rotor-Routing, 𝓁₁-Contraction, Banach Fixed Point}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.39
A Quasi-Polynomial Time Algorithm for Multi-Arrival on Tree-Like Multigraphs

Authors: Ebrahim Ghorbani, Jonah Leander Hoff, and Matthias Mnich

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

Abstract
Propp machines, or rotor-router models, are a classic tool to simulate random systems in forms of Markov chains by deterministic systems. To this end, the nodes of the Markov chain are replaced by switching nodes, which maintain a queue over their outgoing arcs, and a particle sent through the system traverses the top arc of the queue which is then moved to the end of the queue and the particle arrives at the next node. A key question to answer about such systems is whether a single particle can reach a particular target node, given as input an initial configuration of the queues at all switching nodes. This question was introduced by Dohrau et al. (2017) under the name of Arrival. A major open question is whether Arrival can be solved in polynomial time, as it is known to lie in NP ∩ co-NP; yet the fastest known algorithm for general instances takes subexponential time (Gärtner et al., ICALP 2021). We consider a generalized version of Arrival introduced by Auger et al. (RP 2023), which requires routing multiple (potentially exponentially many) particles through a rotor graph. The Multi-Arrival problem is to determine the particle configuration that results from moving all particles from a given initial configuration to sinks. Auger et al. showed that for path-like rotor graphs with a certain uniform rotor order, the problem can be solved in polynomial time. Our main result is a quasi-polynomial-time algorithm for Multi-Arrival on tree-like rotor graphs for arbitrary rotor orders. Tree-like rotor graphs are directed multigraphs which can be obtained from undirected trees by replacing each edge by an arbitrary number of arcs in either or both directions. For trees of bounded contracted height, such as paths, the algorithm runs in polynomial time and thereby generalizes the result by Auger et al.. Moreover, we give a polynomial-time algorithm for Multi-Arrival on tree-like rotor graphs without parallel arcs.
Cite as

Ebrahim Ghorbani, Jonah Leander Hoff, and Matthias Mnich. A Quasi-Polynomial Time Algorithm for Multi-Arrival on Tree-Like Multigraphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghorbani_et_al:LIPIcs.STACS.2025.39,
  author =	{Ghorbani, Ebrahim and Leander Hoff, Jonah and Mnich, Matthias},
  title =	{{A Quasi-Polynomial Time Algorithm for Multi-Arrival on Tree-Like Multigraphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{39:1--39:19},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-228658},
  doi =		{10.4230/LIPIcs.STACS.2025.39},
  annote =	{Keywords: Arrival, Rotor-routing, Tree-like Multigraph, Path-Like Multigraph, Fixed-Parameter Tractability}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.14
The More the Merrier! On Total Coding and Lattice Problems and the Complexity of Finding Multicollisions

Authors: Huck Bennett, Surendra Ghentiyala, and Noah Stephens-Davidowitz

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

Abstract
We show a number of connections between two types of search problems: (1) the problem of finding an L-wise multicollision in the output of a function; and (2) the problem of finding two codewords in a code (or two vectors in a lattice) that are within distance d of each other. Specifically, we study these problems in the total regime, in which L and d are chosen so that such a solution is guaranteed to exist, though it might be hard to find. In more detail, we study the total search problem in which the input is a function 𝒞 : [A] → [B] (represented as a circuit) and the goal is to find L ≤ ⌈A/B⌉ distinct elements x_1,…, x_L ∈ A such that 𝒞(x_1) = ⋯ = 𝒞(x_L). The associated complexity classes Polynomial Multi-Pigeonhole Principle ((A,B)-PMPP^L) consist of all problems that reduce to this problem. We show close connections between (A,B)-PMPP^L and many celebrated upper bounds on the minimum distance of a code or lattice (and on the list-decoding radius). In particular, we show that the associated computational problems (i.e., the problem of finding two distinct codewords or lattice points that are close to each other) are in (A,B)-PMPP^L, with a more-or-less smooth tradeoff between the distance d and the parameters A, B, and L. These connections are particularly rich in the case of codes, in which case we show that multiple incomparable bounds on the minimum distance lie in seemingly incomparable complexity classes. Surprisingly, we also show that the computational problems associated with some bounds on the minimum distance of codes are actually hard for these classes (for codes represented by arbitrary circuits). In fact, we show that finding two vectors within a certain distance d is actually hard for the important (and well-studied) class PWPP = (B²,B)-PMPP² in essentially all parameter regimes for which an efficient algorithm is not known, so that our hardness results are essentially tight. In fact, for some d (depending on the block length, message length, and alphabet size), we obtain both hardness and containment. We therefore completely settle the complexity of this problem for such parameters and add coding problems to the short list of problems known to be complete for PWPP. We also study (A,B)-PMPP^L as an interesting family of complexity classes in its own right, and we uncover a rich structure. Specifically, we use recent techniques from the cryptographic literature on multicollision-resistant hash functions to (1) show inclusions of the form (A,B)-PMPP^L ⊆ (A',B')-PMPP^L' for certain non-trivial parameters; (2) black-box separations between such classes in different parameter regimes; and (3) a non-black-box proof that (A,B)-PMPP^L ∈ FP if (A',B')-PMPP^L' ∈ FP for yet another parameter regime. We also show that (A,B)-PMPP^L lies in the recently introduced complexity class Polynomial Long Choice for some parameters.
Cite as

Huck Bennett, Surendra Ghentiyala, and Noah Stephens-Davidowitz. The More the Merrier! On Total Coding and Lattice Problems and the Complexity of Finding Multicollisions. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bennett_et_al:LIPIcs.ITCS.2025.14,
  author =	{Bennett, Huck and Ghentiyala, Surendra and Stephens-Davidowitz, Noah},
  title =	{{The More the Merrier! On Total Coding and Lattice Problems and the Complexity of Finding Multicollisions}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{14:1--14:22},
  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.2025.14},
  URN =		{urn:nbn:de:0030-drops-226424},
  doi =		{10.4230/LIPIcs.ITCS.2025.14},
  annote =	{Keywords: Multicollisions, Error-correcting codes, Lattices}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.50
One-Way Functions vs. TFNP: Simpler and Improved

Authors: Lukáš Folwarczný, Mika Göös, Pavel Hubáček, Gilbert Maystre, and Weiqiang Yuan

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Simon (1998) proved that it is impossible to construct collision-resistant hash functions from one-way functions using a black-box reduction. It is conjectured more generally that one-way functions do not imply, via a black-box reduction, the hardness of any total NP search problem (collision-resistant hash functions being just one such example). We make progress towards this conjecture by ruling out a large class of "single-query" reductions. In particular, we improve over the prior work of Hubáček et al. (2020) in two ways: our result is established via a novel simpler combinatorial technique and applies to a broader class of semi black-box reductions.
Cite as

Lukáš Folwarczný, Mika Göös, Pavel Hubáček, Gilbert Maystre, and Weiqiang Yuan. One-Way Functions vs. TFNP: Simpler and Improved. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{folwarczny_et_al:LIPIcs.ITCS.2024.50,
  author =	{Folwarczn\'{y}, Luk\'{a}\v{s} and G\"{o}\"{o}s, Mika and Hub\'{a}\v{c}ek, Pavel and Maystre, Gilbert and Yuan, Weiqiang},
  title =	{{One-Way Functions vs. TFNP: Simpler and Improved}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{50:1--50:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.50},
  URN =		{urn:nbn:de:0030-drops-195788},
  doi =		{10.4230/LIPIcs.ITCS.2024.50},
  annote =	{Keywords: TFNP, One-Way Functions, Oracle, Separation, Black-Box}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.63
TFNP Intersections Through the Lens of Feasible Disjunction

Authors: Pavel Hubáček, Erfan Khaniki, and Neil Thapen

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
The complexity class CLS was introduced by Daskalakis and Papadimitriou (SODA 2010) to capture the computational complexity of important TFNP problems solvable by local search over continuous domains and, thus, lying in both PLS and PPAD. It was later shown that, e.g., the problem of computing fixed points guaranteed by Banach’s fixed point theorem is CLS-complete by Daskalakis et al. (STOC 2018). Recently, Fearnley et al. (J. ACM 2023) disproved the plausible conjecture of Daskalakis and Papadimitriou that CLS is a proper subclass of PLS∩PPAD by proving that CLS = PLS∩PPAD. To study the possibility of other collapses in TFNP, we connect classes formed as the intersection of existing subclasses of TFNP with the phenomenon of feasible disjunction in propositional proof complexity; where a proof system has the feasible disjunction property if, whenever a disjunction F ∨ G has a small proof, and F and G have no variables in common, then either F or G has a small proof. Based on some known and some new results about feasible disjunction, we separate the classes formed by intersecting the classical subclasses PLS, PPA, PPAD, PPADS, PPP and CLS. We also give the first examples of proof systems which have the feasible interpolation property, but not the feasible disjunction property.
Cite as

Pavel Hubáček, Erfan Khaniki, and Neil Thapen. TFNP Intersections Through the Lens of Feasible Disjunction. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 63:1-63:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hubacek_et_al:LIPIcs.ITCS.2024.63,
  author =	{Hub\'{a}\v{c}ek, Pavel and Khaniki, Erfan and Thapen, Neil},
  title =	{{TFNP Intersections Through the Lens of Feasible Disjunction}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{63:1--63:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.63},
  URN =		{urn:nbn:de:0030-drops-195917},
  doi =		{10.4230/LIPIcs.ITCS.2024.63},
  annote =	{Keywords: TFNP, feasible disjunction, proof complexity, TFNP intersection classes}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.22
PPP-Completeness and Extremal Combinatorics

Authors: Romain Bourneuf, Lukáš Folwarczný, Pavel Hubáček, Alon Rosen, and Nikolaj I. Schwartzbach

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey’s theorem on monochromatic subgraphs and the Erdős-Rado sunflower lemma. Implicit versions of the corresponding total search problems are known to be PWPP-hard under randomized reductions in the case of Ramsey’s theorem and PWPP-hard in the case of the sunflower lemma; here "implicit” means that the collection is represented by a poly-sized circuit inducing an exponentially large number of objects. We show that several other well-known theorems from extremal combinatorics - including Erdős-Ko-Rado, Sperner, and Cayley’s formula – give rise to complete problems for PWPP and PPP. This is in contrast to the Ramsey and Erdős-Rado problems, for which establishing inclusion in PWPP has remained elusive. Besides significantly expanding the set of problems that are complete for PWPP and PPP, our work identifies some key properties of combinatorial proofs of existence that can give rise to completeness for these classes. Our completeness results rely on efficient encodings for which finding collisions allows extracting the desired substructure. These encodings are made possible by the tightness of the bounds for the problems at hand (tighter than what is known for Ramsey’s theorem and the sunflower lemma). Previous techniques for proving bounds in TFNP invariably made use of structured algorithms. Such algorithms are not known to exist for the theorems considered in this work, as their proofs "from the book" are non-constructive.
Cite as

Romain Bourneuf, Lukáš Folwarczný, Pavel Hubáček, Alon Rosen, and Nikolaj I. Schwartzbach. PPP-Completeness and Extremal Combinatorics. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bourneuf_et_al:LIPIcs.ITCS.2023.22,
  author =	{Bourneuf, Romain and Folwarczn\'{y}, Luk\'{a}\v{s} and Hub\'{a}\v{c}ek, Pavel and Rosen, Alon and Schwartzbach, Nikolaj I.},
  title =	{{PPP-Completeness and Extremal Combinatorics}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.22},
  URN =		{urn:nbn:de:0030-drops-175255},
  doi =		{10.4230/LIPIcs.ITCS.2023.22},
  annote =	{Keywords: total search problems, extremal combinatorics, PPP-completeness}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.67
Downward Self-Reducibility in TFNP

Authors: Prahladh Harsha, Daniel Mitropolsky, and Alon Rosen

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
A problem is downward self-reducible if it can be solved efficiently given an oracle that returns solutions for strictly smaller instances. In the decisional landscape, downward self-reducibility is well studied and it is known that all downward self-reducible problems are in PSPACE. In this paper, we initiate the study of downward self-reducible search problems which are guaranteed to have a solution - that is, the downward self-reducible problems in TFNP. We show that most natural PLS-complete problems are downward self-reducible and any downward self-reducible problem in TFNP is contained in PLS. Furthermore, if the downward self-reducible problem is in TFUP (i.e. it has a unique solution), then it is actually contained in UEOPL, a subclass of CLS. This implies that if integer factoring is downward self-reducible then it is in fact in UEOPL, suggesting that no efficient factoring algorithm exists using the factorization of smaller numbers.
Cite as

Prahladh Harsha, Daniel Mitropolsky, and Alon Rosen. Downward Self-Reducibility in TFNP. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 67:1-67:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{harsha_et_al:LIPIcs.ITCS.2023.67,
  author =	{Harsha, Prahladh and Mitropolsky, Daniel and Rosen, Alon},
  title =	{{Downward Self-Reducibility in TFNP}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{67:1--67:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.67},
  URN =		{urn:nbn:de:0030-drops-175700},
  doi =		{10.4230/LIPIcs.ITCS.2023.67},
  annote =	{Keywords: downward self-reducibility, TFNP, TFUP, factoring, PLS, CLS}
}
Document
DOI: 10.4230/LIPIcs.ITC.2022.6
On the Distributed Discrete Logarithm Problem with Preprocessing

Authors: Pavel Hubáček, Ľubica Jančová, and Veronika Králová

Published in: LIPIcs, Volume 230, 3rd Conference on Information-Theoretic Cryptography (ITC 2022)

Abstract
Protocols solving the Distributed Discrete Logarithm (DDLog) problem are a core component of many recent constructions of group-based homomorphic secret sharing schemes. On a high-level, these protocols enable two parties to transform multiplicative shares of a secret into additive share locally without any communication. Due to their important applications, various generic optimized DDLog protocols were proposed in the literature, culminating in the asymptotically optimal generic protocol of Dinur, Keller, and Klein (J. Cryptol. 2020) solving DDLog in time T with error probability O(W/T²) when the magnitude of the secret is bounded by W. Given that DDLog is solved repeatedly with respect to a fixed group in its applications, a natural approach for improving the efficiency of DDLog protocols could be via leveraging some precomputed group-specific advice. To understand the limitations of this approach, we revisit the distributed discrete logarithm problem in the preprocessing model and study the possible time-space trade-offs for DDLog in the generic group model. As our main result, we show that, in a group of size N, any generic DDLog protocol for secrets of magnitude W with parties running in time T using precomputed group-specific advice of size S has success probability ε = O (T²/W + max{S,log W} ⋅ T²/N) . Thus, assuming N ≥ W log W, we get a lower bound ST² = Ω(ε N) on the time-space trade-off for DDLog protocols using large advice of size S = Ω(N/W). Interestingly, for DDLog protocols using small advice of size S = O(N/W), we get a lower bound T² = Ω(ε W) on the running time, which, in the constant-error regime, asymptotically matches the running time of the DDLog protocol without any advice of Dinur et al. (J. Cryptol. 2020). In other words, we show that generic DDLog protocols achieving constant success probability do not benefit from any advice of size S = O(N/W) in the online phase of the DDLog problem.
Cite as

Pavel Hubáček, Ľubica Jančová, and Veronika Králová. On the Distributed Discrete Logarithm Problem with Preprocessing. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hubacek_et_al:LIPIcs.ITC.2022.6,
  author =	{Hub\'{a}\v{c}ek, Pavel and Jan\v{c}ov\'{a}, \v{L}ubica and Kr\'{a}lov\'{a}, Veronika},
  title =	{{On the Distributed Discrete Logarithm Problem with Preprocessing}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-238-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{230},
  editor =	{Dachman-Soled, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2022.6},
  URN =		{urn:nbn:de:0030-drops-164847},
  doi =		{10.4230/LIPIcs.ITC.2022.6},
  annote =	{Keywords: Distributed discrete logarithm problem, preprocessing, generic group model}
}
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