60 Search Results for "Fortnow, Lance"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.42
Time and Space Efficient Deterministic List Decoding

Authors: Joshua Cook and Dana Moshkovitz

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

Abstract
Error correcting codes encode messages by codewords in such a way that even if some of the codeword is corrupted, the message can be decoded. Typical decoding algorithms for error correcting codes either use linear space or quadratic time. A natural question is whether codes can be decoded in near-linear time and sub-linear space simultaneously. A recent result by Cook and Moshkovitz gave efficient decoders that can uniquely decode Reed-Muller and other codes from a constant fraction (less than half) of corruption. In this work, we address the problem of list decoding in near-linear time and sub-linear space. In the list decoding setting, most of the codeword is corrupted, and one wants to output a short list of potential messages that contains the true message. For any constants γ, τ > 0, we give decoders for Reed-Muller codes that can decode from 1-γ fraction of corruptions in time n^{1+τ} and space n^{τ}. Our decoders work by extending the iterative correction technique of Cook and Moshkovitz. However, that technique, which gradually decreases the number of corruptions in the message, was tailored to the unique decoding setting. We first identify an intermediate problem, codewords list recovery, for which we can make iterative correction work. We then show how to reduce general list decoding to the codewords list recovery problem in efficient time and space. The reduction relies on local correction and testing. In the codewords list recovery problem, the input consists of n unordered lists containing exactly the symbols from L codewords, where a small fraction of the lists is corrupted. The goal is to find the L codewords. In addition, we prove that any linear code with time-space efficient encoding or decoding must be local, in the sense that the codewords satisfy a local linear constraint. This rules out codes like Reed-Solomon from having time-space efficient encoding or decoding.
Cite as

Joshua Cook and Dana Moshkovitz. Time and Space Efficient Deterministic List Decoding. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 42:1-42:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{cook_et_al:LIPIcs.ITCS.2026.42,
  author =	{Cook, Joshua and Moshkovitz, Dana},
  title =	{{Time and Space Efficient Deterministic List Decoding}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{42:1--42:24},
  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.2026.42},
  URN =		{urn:nbn:de:0030-drops-253292},
  doi =		{10.4230/LIPIcs.ITCS.2026.42},
  annote =	{Keywords: Reed-Muller code, local correction, local testing}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.10
On the Complexity of Unique Quantum Witnesses and Quantum Approximate Counting

Authors: Anurag Anshu, Jonas Haferkamp, Yeongwoo Hwang, and Quynh T. Nguyen

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

Abstract
We study the long-standing open question on the power of unique witnesses in quantum protocols, which asks if UniqueQMA, a variant of QMA whose accepting witness space is 1-dimensional, contains QMA under quantum reductions. This work rules out any black-box reduction from QMA to UniqueQMA by showing a quantum oracle separation between BQP^UniqueQMA and QMA. This provides a contrast to the classical case, where the Valiant-Vazirani theorem shows a black-box randomized reduction from UniqueNP to NP, and suggests the need for studying the structure of the ground space of local Hamiltonians in distilling a potential unique witness. Via similar techniques, we show, relative to a quantum oracle, that QMA^QMA cannot decide quantum approximate counting, ruling out a quantum analogue of Stockmeyer’s algorithm in the black-box setting. Our results employ a subspace reflection oracle, previously considered in [Scott Aaronson and Greg Kuperberg, 2007; Scott Aaronson et al., 2020; She and Yuen, 2023], but we introduce new tools which allow us to exploit the unique witness constraint. We also show a strong "polarization" behavior of QMA circuits, which could be of independent interest in studying quantum polynomial hierarchies. We then ask a natural question; what structural properties of the local Hamiltonian problem can we exploit? We introduce a physically motivated candidate by showing that the ground energy of local Hamiltonians that satisfy a computational variant of the eigenstate thermalization hypothesis (ETH) can be estimated through a UniqueQMA protocol. Our protocol can be viewed as a quantum expander test in a low energy subspace of the Hamiltonian and verifies a unique entangled state across two copies of the subspace. This allows us to conclude that if UniqueQMA is not equivalent to QMA, then QMA-hard Hamiltonians must violate ETH under adversarial perturbations (more accurately, further assuming the quantum PCP conjecture if ETH only applies to extensive energy subspaces). Under the same assumption, this also serves as evidence that chaotic local Hamiltonians, such as the SYK model may be computationally simpler than general local Hamiltonians.
Cite as

Anurag Anshu, Jonas Haferkamp, Yeongwoo Hwang, and Quynh T. Nguyen. On the Complexity of Unique Quantum Witnesses and Quantum Approximate Counting. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{anshu_et_al:LIPIcs.ITCS.2026.10,
  author =	{Anshu, Anurag and Haferkamp, Jonas and Hwang, Yeongwoo and Nguyen, Quynh T.},
  title =	{{On the Complexity of Unique Quantum Witnesses and Quantum Approximate Counting}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{10:1--10:20},
  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.2026.10},
  URN =		{urn:nbn:de:0030-drops-252978},
  doi =		{10.4230/LIPIcs.ITCS.2026.10},
  annote =	{Keywords: Quantum complexity, approximate counting, Valiant-Vazirani, eigenstate thermalization hypothesis}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.62
Improved Rate for Non-Malleable Codes and Time-Lock Puzzles

Authors: Cody Freitag, Ilan Komargodski, Manu Kondapaneni, and Jad Silbak

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

Abstract
Non-malleable codes allow a sender to transmit a message to a receiver, while providing a "best-possible" integrity guarantee to ensure that no attacker - who cannot already decode the message - can meaningfully tamper the message in transit. If tampered, the received message should either be invalid or unrelated to the original message. Non-malleable time-lock puzzles (TLPs) are a special case of non-malleable codes for bounded polynomial-depth tampering with very efficient encoding. In this work, we give generic techniques for constructing non-malleable codes and non-malleable TLPs with improved rate, which captures the ratio of a message’s length to its encoding length. A key contribution of our work is identifying a security notion for non-malleability, which we term "CCA-hiding", sufficient for our compilers. CCA-hiding is a relaxation of CCA-security for encryption or commitments to the fine-grained setting of codes, and requires that the encoded message remains hidden, even given a decoding oracle for any other codeword. Intriguingly, CCA-hiding does not imply non-malleability in the fine-grained setting, as is the case for encryption and commitments. Using our new techniques, we give the following constructions: - Rate-1 CCA-hiding TLPs in the plain model. - Rate-1 non-malleable codes for bounded polynomial-depth tampering in the auxiliary-input random oracle model (AI-ROM). - Rate-(1/2) non-malleable TLPs in the AI-ROM.
Cite as

Cody Freitag, Ilan Komargodski, Manu Kondapaneni, and Jad Silbak. Improved Rate for Non-Malleable Codes and Time-Lock Puzzles. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 62:1-62:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{freitag_et_al:LIPIcs.ITCS.2026.62,
  author =	{Freitag, Cody and Komargodski, Ilan and Kondapaneni, Manu and Silbak, Jad},
  title =	{{Improved Rate for Non-Malleable Codes and Time-Lock Puzzles}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{62:1--62:24},
  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.2026.62},
  URN =		{urn:nbn:de:0030-drops-253490},
  doi =		{10.4230/LIPIcs.ITCS.2026.62},
  annote =	{Keywords: Non-malleable codes, Time-lock puzzles}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.111
Hardness of Range Avoidance and Proof Complexity Generators from Demi-Bits

Authors: Hanlin Ren, Yichuan Wang, and Yan Zhong

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

Abstract
Given a circuit G: {0, 1}ⁿ → {0, 1}^m with m > n, the range avoidance problem (Avoid) asks to output a string y ∈ {0, 1}^m that is not in the range of G. Besides its profound connection to circuit complexity and explicit construction problems, this problem is also related to the existence of proof complexity generators - circuits G: {0, 1}ⁿ → {0, 1}^m where m > n but for every y ∈ {0, 1}^m, it is infeasible to prove the statement "y ̸ ∈ Range(G)" in a given propositional proof system. This paper connects these two problems with the existence of demi-bits generators, a fundamental cryptographic primitive against nondeterministic adversaries introduced by Rudich (RANDOM '97). - We show that the existence of demi-bits generators implies Avoid is hard for nondeterministic algorithms. This resolves an open problem raised by Chen and Li (STOC '24). Furthermore, assuming the demi-hardness of certain LPN-style generators or Goldreich’s PRG, we prove the hardness of Avoid even when the instances are constant-degree polynomials over 𝔽₂. - We show that the dual weak pigeonhole principle is unprovable in Cook’s theory PV₁ under the existence of demi-bits generators secure against AM/_{O(1)}, thereby separating Jeřábek’s theory APC₁ from PV₁. Previously, Ilango, Li, and Williams (STOC '23) obtained the same separation under different (and arguably stronger) cryptographic assumptions. - We transform demi-bits generators to proof complexity generators that are pseudo-surjective in certain parameter regime. Pseudo-surjectivity is the strongest form of hardness considered in the literature for proof complexity generators. Our constructions are inspired by the recent breakthroughs on the hardness of Avoid by Ilango, Li, and Williams (STOC '23) and Chen and Li (STOC '24). We use randomness extractors to significantly simplify the construction and the proof.
Cite as

Hanlin Ren, Yichuan Wang, and Yan Zhong. Hardness of Range Avoidance and Proof Complexity Generators from Demi-Bits. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 111:1-111:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{ren_et_al:LIPIcs.ITCS.2026.111,
  author =	{Ren, Hanlin and Wang, Yichuan and Zhong, Yan},
  title =	{{Hardness of Range Avoidance and Proof Complexity Generators from Demi-Bits}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{111:1--111:25},
  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.2026.111},
  URN =		{urn:nbn:de:0030-drops-253982},
  doi =		{10.4230/LIPIcs.ITCS.2026.111},
  annote =	{Keywords: Range Avoidance, Proof Complexity Generators}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.34
Testing Classical Properties from Quantum Data

Authors: Matthias C. Caro, Preksha Naik, and Joseph Slote

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

Abstract
Many properties of Boolean functions can be tested far more efficiently than the function itself can be learned. However, this dramatic advantage often disappears when testers are limited to random samples of f instead of adaptively chosen queries to f. In this work we investigate the quantum version of this restriction: quantum algorithms that test properties of a Boolean function f solely from copies of either the function state |f⟩∝ ∑_x|x,f(x)⟩ or the phase state |(-1)^f⟩∝ ∑_x (-1)^{f(x)}|x⟩. Quantum advantage in testing from data. For monotonicity, symmetry, and triangle-freeness, we show passive quantum testers are unboundedly or super-polynomially better than their classical passive testing counterparts. They are competitive with classic query-based testers in each case. Inadequacy of Fourier sampling. Our new testers use techniques beyond quantum Fourier sampling, and it turns out this is necessary: we show a certain class of bent functions can be tested from 𝒪(1) function states but has a sample complexity lower bound of 2^{Ω(n)} for any tester relying exclusively on Fourier and classical samples. Classical queries vs. quantum data. Our passive quantum testers are competitive with classical query-based testers, but this isn't universal: we exhibit a testing problem that can be solved from 𝒪(1) classical queries but requires Ω(2^{n/2}) function state copies. The Forrelation problem provides a separation of the same magnitude in the opposite direction, so we conclude that quantum data and classical queries are "maximally incomparable" resources for testing. Towards lower bounds. We also begin the study of lower bounds for testing from quantum data. For quantum monotonicity testing, we prove that the ensembles of [Goldreich et al., 2000; Black, 2024], which give exponential lower bounds for classical sample-based testing, do not yield any nontrivial lower bounds for testing from quantum data. New insights specific to quantum data will be required for proving copy complexity lower bounds for testing in this model.
Cite as

Matthias C. Caro, Preksha Naik, and Joseph Slote. Testing Classical Properties from Quantum Data. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 34:1-34:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{caro_et_al:LIPIcs.ITCS.2026.34,
  author =	{Caro, Matthias C. and Naik, Preksha and Slote, Joseph},
  title =	{{Testing Classical Properties from Quantum Data}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{34:1--34:26},
  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.2026.34},
  URN =		{urn:nbn:de:0030-drops-253213},
  doi =		{10.4230/LIPIcs.ITCS.2026.34},
  annote =	{Keywords: Quantum Property Testing, Quantum Data, Boolean Functions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.18
Interactive Proofs for Distribution Testing with Conditional Oracles

Authors: Ari Biswas, Mark Bun, Clément L. Canonne, and Satchit Sivakumar

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

Abstract
We revisit the framework of interactive proofs for distribution testing, first introduced by Chiesa and Gur (ITCS 2018), which has recently experienced a surge in interest, accompanied by notable progress (e.g., Herman and Rothblum, STOC 2022, FOCS 2023; Herman, RANDOM 2024). In this model, a data-poor verifier determines whether a probability distribution has a property of interest by interacting with an all-powerful, data-rich but untrusted prover bent on convincing them that it has the property. While prior work gave sample-, time-, and communication-efficient protocols for testing and estimating a range of distribution properties, they all suffer from an inherent issue: for most interesting properties of distributions over a domain of size N, the verifier must draw at least Ω(√N) samples of its own. While sublinear in N, this is still prohibitive for large domains encountered in practice. In this work, we circumvent this limitation by augmenting the verifier with the ability to perform an exponentially smaller number of more powerful (but reasonable) pairwise conditional queries, effectively enabling them to perform "local comparison checks" of the prover’s claims. We systematically investigate the landscape of interactive proofs in this new setting, giving poly-logarithmic query and sample protocols for (tolerantly) testing all label-invariant properties, thus demonstrating exponential savings without compromising on communication, for this large and fundamental class of testing tasks.
Cite as

Ari Biswas, Mark Bun, Clément L. Canonne, and Satchit Sivakumar. Interactive Proofs for Distribution Testing with Conditional Oracles. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{biswas_et_al:LIPIcs.ITCS.2026.18,
  author =	{Biswas, Ari and Bun, Mark and Canonne, Cl\'{e}ment L. and Sivakumar, Satchit},
  title =	{{Interactive Proofs for Distribution Testing with Conditional Oracles}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{18:1--18:13},
  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.2026.18},
  URN =		{urn:nbn:de:0030-drops-253059},
  doi =		{10.4230/LIPIcs.ITCS.2026.18},
  annote =	{Keywords: Distribution Testing, Interactive Proofs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.37
New Algebrization Barriers to Circuit Lower Bounds via Communication Complexity of Missing-String

Authors: Lijie Chen, Yang Hu, and Hanlin Ren

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

Abstract
The algebrization barrier, proposed by Aaronson and Wigderson (STOC '08, ToCT '09), captures the limitations of many complexity-theoretic techniques based on arithmetization. Notably, several circuit lower bounds that overcome the relativization barrier (Buhrman-Fortnow-Thierauf, CCC '98; Vinodchandran, TCS '05; Santhanam, STOC '07, SICOMP '09) remain subject to the algebrization barrier. In this work, we establish several new algebrization barriers to circuit lower bounds by studying the communication complexity of the following problem, called XOR-Missing-String: For m < 2^{n/2}, Alice gets a list of m strings x₁, … , x_m ∈ {0, 1}ⁿ, Bob gets a list of m strings y₁, … , y_m ∈ {0, 1}ⁿ, and the goal is to output a string s ∈ {0, 1}ⁿ that is not equal to x_i⊕ y_j for any i, j ∈ [m]. 1) We construct an oracle A₁ and its multilinear extension A₁̃ such that PostBPE^{A₁̃} has linear-size A₁-oracle circuits on infinitely many input lengths. That is, proving PostBPE ̸ ⊆ i.o.- SIZE[O(n)] requires non-algebrizing techniques. This barrier follows from a PostBPP communication lower bound for XOR-Missing-String. This is in contrast to the well-known algebrizing lower bound MA_E (⊆ PostBPE) ̸ ⊆ P/_poly. 2) We construct an oracle A₂ and its multilinear extension A₂̃ such that BPE^{A₂̃} has linear-size A₂-oracle circuits on all input lengths. Previously, a similar barrier was demonstrated by Aaronson and Wigderson, but in their result, A₂̃ is only a multiquadratic extension of A₂. Our results show that communication complexity is more useful than previously thought for proving algebrization barriers, as Aaronson and Wigderson wrote that communication-based barriers were "more contrived". This serves as an example of how XOR-Missing-String forms new connections between communication lower bounds and algebrization barriers. 3) Finally, we study algebrization barriers to circuit lower bounds for MA_E. Buhrman, Fortnow, and Thierauf proved a sub-half-exponential circuit lower bound for MA_E via algebrizing techniques. Toward understanding whether the half-exponential bound can be improved, we define a natural subclass of MA_E that includes their hard MA_E language, and prove the following result: For every super-half-exponential function h(n), we construct an oracle A₃ and its multilinear extension A₃̃ such that this natural subclass of MA_E^{A₃̃} has h(n)-size A₃-oracle circuits on all input lengths. This suggests that half-exponential might be the correct barrier for MA_E circuit lower bounds w.r.t. algebrizing techniques.
Cite as

Lijie Chen, Yang Hu, and Hanlin Ren. New Algebrization Barriers to Circuit Lower Bounds via Communication Complexity of Missing-String. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 37:1-37:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.ITCS.2026.37,
  author =	{Chen, Lijie and Hu, Yang and Ren, Hanlin},
  title =	{{New Algebrization Barriers to Circuit Lower Bounds via Communication Complexity of Missing-String}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{37:1--37:20},
  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.2026.37},
  URN =		{urn:nbn:de:0030-drops-253246},
  doi =		{10.4230/LIPIcs.ITCS.2026.37},
  annote =	{Keywords: circuit lower bound, algebrization barrier, missing string, communication complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.13
Optimal Online Bipartite Matching in Degree-2 Graphs

Authors: Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha

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

Abstract
Online bipartite matching is a classical problem in online algorithms and we know that both the deterministic fractional and randomized integral online matchings achieve the same competitive ratio of 1-1/e. In this work, we study classes of graphs where the online degree is restricted to 2. As expected, one can achieve a competitive ratio of better than 1-1/e in both the deterministic fractional and randomized integral cases, but surprisingly, these ratios are not the same. It was already known that for fractional matching, a 0.75 competitive ratio algorithm is optimal. We show that the folklore Half-Half algorithm achieves a competitive ratio of η ≈ 0.717772… and more surprisingly, show that this is optimal by giving a matching lower-bound. This yields a separation between the two problems: deterministic fractional and randomized integral, showing that it is impossible to obtain a perfect rounding scheme.
Cite as

Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha. Optimal Online Bipartite Matching in Degree-2 Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bhangale_et_al:LIPIcs.ISAAC.2025.13,
  author =	{Bhangale, Amey and Chakraborty, Arghya and Harsha, Prahladh},
  title =	{{Optimal Online Bipartite Matching in Degree-2 Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.13},
  URN =		{urn:nbn:de:0030-drops-249216},
  doi =		{10.4230/LIPIcs.ISAAC.2025.13},
  annote =	{Keywords: Online Algorithm, Bipartite matching}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.77
Tolerant Testers for Subgraph-Freeness

Authors: Reut Levi and Jonathan Meiri

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

Abstract
In this paper we study the problem of tolerantly testing the property of being H-free (which also implies distance approximation from being H-free). In the general-graphs model, we show that for tolerant K_k-freeness testing can be achieved with query complexity that is polynomial in the arboricity of the input graph G, arb(G), and independent of the size of G (for graphs in which the average degree is Ω(1)). Specifically for triangles, our algorithm distinguished graphs which are ε-close to being triangle-free from graphs that 3ε(1+η)-far from being triangle-free with expected query complexity which is Õ(arb³(G)) (for constant η and ε). For general k-cliques our algorithm distinguishes graphs which are ε-close to being K_k-free from graphs which are binom(k,2)ε(1+η)-far from being K_k-free with expected query complexity which is polynomial in k, ε, γ and arb(G). We then generalize our result and provide a similar result for any motif H which is 2-connected of radius 1. This includes for example the wheel-graph. Finally, we show that our tester can be applied to the bounded-degree model for tolerantly testing H-freeness for any motif H. The query complexity of the algorithm is polynomial in the degree bound, d, improving the previous state-of-the-art by Marko and Ron (TALG 2009) that obtained quasi-polynomial query complexity in d.
Cite as

Reut Levi and Jonathan Meiri. Tolerant Testers for Subgraph-Freeness. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 77:1-77:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{levi_et_al:LIPIcs.ESA.2025.77,
  author =	{Levi, Reut and Meiri, Jonathan},
  title =	{{Tolerant Testers for Subgraph-Freeness}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{77:1--77:15},
  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.2025.77},
  URN =		{urn:nbn:de:0030-drops-245456},
  doi =		{10.4230/LIPIcs.ESA.2025.77},
  annote =	{Keywords: Tolerant Testing, Property Testing, Subgraph freeness, distance approximation, arboricity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.84
Property Testing of Curve Similarity

Authors: Peyman Afshani, Maike Buchin, Anne Driemel, Marena Richter, and Sampson Wong

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

Abstract
We propose sublinear algorithms for probabilistic testing of the discrete and continuous Fréchet distance - a standard similarity measure for curves. We assume the algorithm is given access to the input curves via a query oracle: a query returns the set of vertices of the curve that lie within a radius δ of a specified vertex of the other curve. The goal is to use a small number of queries to determine with constant probability whether the two curves are similar (i.e., their discrete Fréchet distance is at most δ) or they are "ε-far" (for 0 < ε < 2) from being similar, i.e., more than an ε-fraction of the two curves must be ignored for them to become similar. We present two algorithms which are sublinear assuming that the curves are t-approximate shortest paths in the ambient metric space, for some t ≪ n. The first algorithm uses O(t/ε log t/ε) queries and is given the value of t in advance. The second algorithm does not have explicit knowledge of the value of t and therefore needs to gain implicit knowledge of the straightness of the input curves through its queries. We show that the discrete Fréchet distance can still be tested using roughly O({t³+t² log n}/ε) queries ignoring logarithmic factors in t. Our algorithms work in a matrix representation of the input and may be of independent interest to matrix testing. Our algorithms use a mild uniform sampling condition that constrains the edge lengths of the curves, similar to a polynomially bounded aspect ratio. Applied to testing the continuous Fréchet distance of t-straight curves, our algorithms can be used for (1+ε')-approximate testing using essentially the same bounds as stated above with an additional factor of poly(1/(ε')).
Cite as

Peyman Afshani, Maike Buchin, Anne Driemel, Marena Richter, and Sampson Wong. Property Testing of Curve Similarity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 84:1-84:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{afshani_et_al:LIPIcs.ESA.2025.84,
  author =	{Afshani, Peyman and Buchin, Maike and Driemel, Anne and Richter, Marena and Wong, Sampson},
  title =	{{Property Testing of Curve Similarity}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{84:1--84:16},
  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.2025.84},
  URN =		{urn:nbn:de:0030-drops-245522},
  doi =		{10.4230/LIPIcs.ESA.2025.84},
  annote =	{Keywords: Fr\'{e}chet distance, Trajectory Analysis, Curve Similarity, Property Testing, Monotonicity Testing}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.32
Quantum Property Testing in Sparse Directed Graphs

Authors: Simon Apers, Frédéric Magniez, Sayantan Sen, and Dániel Szabó

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

Abstract
We initiate the study of quantum property testing in sparse directed graphs, and more particularly in the unidirectional model, where the algorithm is allowed to query only the outgoing edges of a vertex. In the classical unidirectional model, the problem of testing k-star-freeness, and more generally k-source-subgraph-freeness, is almost maximally hard for large k. We prove that this problem has almost quadratic advantage in the quantum setting. Moreover, we show that this advantage is nearly tight, by showing a quantum lower bound using the method of dual polynomials on an intermediate problem for a new, property testing version of the k-collision problem that was not studied before. To illustrate that not all problems in graph property testing admit such a quantum speedup, we consider the problem of 3-colorability in the related undirected bounded-degree model, when graphs are now undirected. This problem is maximally hard to test classically, and we show that also quantumly it requires a linear number of queries.
Cite as

Simon Apers, Frédéric Magniez, Sayantan Sen, and Dániel Szabó. Quantum Property Testing in Sparse Directed Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 32:1-32:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{apers_et_al:LIPIcs.APPROX/RANDOM.2025.32,
  author =	{Apers, Simon and Magniez, Fr\'{e}d\'{e}ric and Sen, Sayantan and Szab\'{o}, D\'{a}niel},
  title =	{{Quantum Property Testing in Sparse Directed Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{32:1--32:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.32},
  URN =		{urn:nbn:de:0030-drops-243987},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.32},
  annote =	{Keywords: property testing, quantum computing, bounded-degree directed graphs, dual polynomial method, collision finding}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.59
Testing Tensor Products of Algebraic Codes

Authors: Sumegha Garg, Madhu Sudan, and Gabriel Wu

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

Abstract
Motivated by recent advances in locally testable codes and quantum LDPCs based on robust testability of tensor product codes, we explore the local testability of tensor products of (an abstraction of) algebraic geometry codes. Such codes are parameterized by, in addition to standard parameters such as block length n and dimension k, their genus g. We show that the tensor product of two algebraic geometry codes is robustly locally testable provided n = Ω((k+g)²). Apart from Reed-Solomon codes, this seems to be the first explicit family of two-wise tensor codes of high dual distance that is robustly locally testable by the natural test that measures the expected distance of a random row/column from the underlying code.
Cite as

Sumegha Garg, Madhu Sudan, and Gabriel Wu. Testing Tensor Products of Algebraic Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 59:1-59:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{garg_et_al:LIPIcs.APPROX/RANDOM.2025.59,
  author =	{Garg, Sumegha and Sudan, Madhu and Wu, Gabriel},
  title =	{{Testing Tensor Products of Algebraic Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{59:1--59:12},
  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.2025.59},
  URN =		{urn:nbn:de:0030-drops-244254},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.59},
  annote =	{Keywords: Algebraic geometry codes, Robust testability, Tensor products of codes}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.84
Algebraic Barriers to Halving Algorithmic Information Quantities in Correlated Strings

Authors: Andrei Romashchenko

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

Abstract
We study the possibility of scaling down algorithmic information quantities in tuples of correlated strings. In particular, we address a question raised by Alexander Shen: whether, for any triple of strings (a, b, c), there exists a string z such that each conditional Kolmogorov complexity C(a|z), C(b|z), C(c|z) is approximately half of the corresponding unconditional Kolmogorov complexity. We provide a negative answer to this question by constructing a triple (a, b, c) for which no such string z exists. Our construction is based on combinatorial properties of incidences in finite projective planes and relies on recent bounds for point-line incidences over prime fields, obtained using tools from additive combinatorics and algebraic methods, notably results by Bourgain-Katz-Tao and Stevens-De Zeeuw. As an application, we show that this impossibility yields lower bounds on the communication complexity of secret key agreement protocols in certain settings. These results reveal algebraic obstructions to efficient information exchange and highlight a separation in information-theoretic behavior between fields with and without proper subfields.
Cite as

Andrei Romashchenko. Algebraic Barriers to Halving Algorithmic Information Quantities in Correlated Strings. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 84:1-84:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{romashchenko:LIPIcs.MFCS.2025.84,
  author =	{Romashchenko, Andrei},
  title =	{{Algebraic Barriers to Halving Algorithmic Information Quantities in Correlated Strings}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{84:1--84:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.84},
  URN =		{urn:nbn:de:0030-drops-241914},
  doi =		{10.4230/LIPIcs.MFCS.2025.84},
  annote =	{Keywords: Kolmogorov complexity, algorithmic information theory, communication complexity, discrete geometry}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.31
Towards Free Lunch Derandomization from Necessary Assumptions (And OWFs)

Authors: Marshall Ball, Lijie Chen, and Roei Tell

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
The question of optimal derandomization, introduced by Doron et. al (JACM 2022), garnered significant recent attention. Works in recent years showed conditional superfast derandomization algorithms, as well as conditional impossibility results, and barriers for obtaining superfast derandomization using certain black-box techniques. Of particular interest is the extreme high-end, which focuses on "free lunch" derandomization, as suggested by Chen and Tell (FOCS 2021). This is derandomization that incurs essentially no time overhead, and errs only on inputs that are infeasible to find. Constructing such algorithms is challenging, and so far there have not been any results following the one in their initial work. In their result, their algorithm is essentially the classical Nisan-Wigderson generator, and they relied on an ad-hoc assumption asserting the existence of a function that is non-batch-computable over all polynomial-time samplable distributions. In this work we deduce free lunch derandomization from a variety of natural hardness assumptions. In particular, we do not resort to non-batch-computability, and the common denominator for all of our assumptions is hardness over all polynomial-time samplable distributions, which is necessary for the conclusion. The main technical components in our proofs are constructions of new and superfast targeted generators, which completely eliminate the time overheads that are inherent to all previously known constructions. In particular, we present an alternative construction for the targeted generator by Chen and Tell (FOCS 2021), which is faster than the original construction, and also more natural and technically intuitive. These contributions significantly strengthen the evidence for the possibility of free lunch derandomization, distill the required assumptions for such a result, and provide the first set of dedicated technical tools that are useful for studying the question.
Cite as

Marshall Ball, Lijie Chen, and Roei Tell. Towards Free Lunch Derandomization from Necessary Assumptions (And OWFs). In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{ball_et_al:LIPIcs.CCC.2025.31,
  author =	{Ball, Marshall and Chen, Lijie and Tell, Roei},
  title =	{{Towards Free Lunch Derandomization from Necessary Assumptions (And OWFs)}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{31:1--31:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.31},
  URN =		{urn:nbn:de:0030-drops-237259},
  doi =		{10.4230/LIPIcs.CCC.2025.31},
  annote =	{Keywords: Pseudorandomness, Derandomization}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.24
Super-Critical Trade-Offs in Resolution over Parities via Lifting

Authors: Arkadev Chattopadhyay and Pavel Dvořák

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Razborov [Alexander A. Razborov, 2016] exhibited the following surprisingly strong trade-off phenomenon in propositional proof complexity: for a parameter k = k(n), there exists k-CNF formulas over n variables, having resolution refutations of O(k) width, but every tree-like refutation of width n^{1-ε}/k needs size exp(n^Ω(k)). We extend this result to tree-like Resolution over parities, commonly denoted by Res(⊕), with parameters essentially unchanged. To obtain our result, we extend the lifting theorem of Chattopadhyay, Mande, Sanyal and Sherif [Arkadev Chattopadhyay et al., 2023] to handle tree-like affine DAGs. We introduce additional ideas from linear algebra to handle forget nodes along long paths.
Cite as

Arkadev Chattopadhyay and Pavel Dvořák. Super-Critical Trade-Offs in Resolution over Parities via Lifting. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chattopadhyay_et_al:LIPIcs.CCC.2025.24,
  author =	{Chattopadhyay, Arkadev and Dvo\v{r}\'{a}k, Pavel},
  title =	{{Super-Critical Trade-Offs in Resolution over Parities via Lifting}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.24},
  URN =		{urn:nbn:de:0030-drops-237186},
  doi =		{10.4230/LIPIcs.CCC.2025.24},
  annote =	{Keywords: Proof complexity, Lifting, Resolution over parities}
}
  • Refine by Type
  • 60 Document/PDF
  • 31 Document/HTML

  • Refine by Publication Year
  • 7 2026
  • 24 2025
  • 1 2024
  • 2 2022
  • 1 2021
  • Show More...

  • Refine by Author
  • 9 Fortnow, Lance
  • 8 Buhrman, Harry
  • 7 Thierauf, Thomas
  • 4 Agrawal, Manindra
  • 3 Aaronson, Scott
  • Show More...

  • Refine by Series/Journal
  • 38 LIPIcs
  • 1 DagSemRep
  • 21 DagSemProc

  • Refine by Classification
  • 7 Theory of computation → Complexity classes
  • 6 Theory of computation → Quantum complexity theory
  • 5 Theory of computation → Computational complexity and cryptography
  • 5 Theory of computation → Streaming, sublinear and near linear time algorithms
  • 4 Theory of computation → Circuit complexity
  • Show More...

  • Refine by Keyword
  • 5 quantum computing
  • 4 Computational complexity
  • 3 Computational Complexity
  • 3 Kolmogorov complexity
  • 3 Property Testing
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact