24 Search Results for "Zhang, Jiapeng"

Document
DOI: 10.4230/LIPIcs.STACS.2026.28
Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank

Authors: Nikolai Chukhin, Alexander S. Kulikov, Ivan Mihajlin, and Arina Smirnova

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

Abstract
Proving complexity lower bounds remains a challenging task: currently, we only know how to prove conditional uniform (algorithm) lower bounds and nonuniform (circuit) lower bounds in restricted circuit models. About a decade ago, Williams (STOC 2010) showed how to derive nonuniform lower bounds from uniform upper bounds: roughly, by designing a fast algorithm for checking satisfiability of circuits, one gets a lower bound for this circuit class. Since then, a number of results of this kind have been proved. For example, Jahanjou et al. (ICALP 2015) and Carmosino et al. (ITCS 2016) proved that if NSETH fails, then E^{NP} has series-parallel circuit size ω(n). One can also derive nonuniform lower bounds from nondeterministic uniform lower bounds. Perhaps the most well-known example is the Karp-Lipton theorem (STOC 1980): if Σ₂ ≠ Π₂, then NP ⊄ P/poly. Some recent examples include the following. Nederlof (STOC 2020) proved a lower bound on the matrix multiplication tensor rank under an assumption that TSP cannot be solved faster than in 2ⁿ time. Belova et al. (SODA 2024) proved that there exists an explicit polynomial family of arithmetic circuit size Ω(n^{δ}), for any δ > 0, assuming that MAX-3-SAT cannot be solved faster than in 2ⁿ nondeterministic time. Williams (FOCS 2024) proved an exponential lower bound for ETHR ∘ ETHR circuits under the Orthogonal Vectors conjecture. Whereas all the lower bounds above are proved under strong assumptions that might eventually be refuted, the revealed connections are of great interest and may still give further insights: one may be able to weaken the used assumptions or to construct generators from other fine-grained reductions. In this paper, we continue developing this line of research and show how uniform nondeterministic lower bounds can be used to construct generators of various types of combinatorial objects that are notoriously hard to analyze: Boolean functions of high circuit size, matrices of high rigidity, and tensors of high rank. Specifically, we prove the following. - If, for some ε and k, k-SAT cannot be solved in input-oblivious co-nondeterministic time O(2^{(1/2+ε)n}), then there exists a monotone Boolean function family in coNP of monotone circuit size 2^{Ω(n / log n)}. Combining this with the result above, we get win-win circuit lower bounds: either E^{NP{}} requires series-parallel circuits of size ω(n) or coNP requires monotone circuits of size 2^{Ω(n / log n)}. - If, for all ε > 0, MAX-3-SAT cannot be solved in co-nondeterministic time O(2^{(1 - ε)n}), then there exist small families of matrices with rigidity exceeding the best known constructions as well as small families of three-dimensional tensors of rank n^{1+Δ}, for some Δ > 0.
Cite as

Nikolai Chukhin, Alexander S. Kulikov, Ivan Mihajlin, and Arina Smirnova. Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chukhin_et_al:LIPIcs.STACS.2026.28,
  author =	{Chukhin, Nikolai and Kulikov, Alexander S. and Mihajlin, Ivan and Smirnova, Arina},
  title =	{{Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{28:1--28:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.28},
  URN =		{urn:nbn:de:0030-drops-255177},
  doi =		{10.4230/LIPIcs.STACS.2026.28},
  annote =	{Keywords: computational complexity, circuit complexity, lower bounds, conditional lower bounds, monotone circuits, matrix rigidity, tensor rank, arithmetic circuits, fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.110
Optimal Two-Round Communication Lower Bound for Graph Connectivity via Pointer Chasing

Authors: Jaikumar Radhakrishnan, Chaitanya Reddy, and Rakesh Venkat

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

Abstract
We consider the communication complexity of the graph connectivity problem, where the edges of an n-vertex undirected graph G are distributed between two parties Alice and Bob, who are then required to communicate to determine if G is connected. We show that in any randomized protocol with two-rounds of communication, Alice and Bob must exchange Ω(nlog n) bits; such a lower bound for one-round protocols was shown by Sun and Woodruff (APPROX/RANDOM 2015). A one-round deterministic protocol, where Alice sends O(n log n) bits and Bob determines the answer, was observed by Hajnal, Maass and Turan (STOC 1988); they also showed a matching lower bound of Ω(n log n) bits for deterministic protocols with unbounded rounds of communication. For randomized protocols, a reduction from the set disjointness problem due to Babai, Frankl and Simon (FOCS 1986) implies a randomized lower bound of Ω(n) even with unbounded rounds of communication. Whether this lower bound can be improved to Ω(n log n) has been an outstanding open question, whose algorithmic implications were recently emphasized by Apers, Efron, Gawrychowski, Lee, Mukopadhyay and Nanongkai (FOCS 2022). Our lower bound for randomized two-round protocols is based on a reduction from a restricted version of the two-player pointer chasing problem originally studied by Papadimitriou and Sipser (JCSS 1984). Using this reduction, we show an ω(n) lower bounds on graph connectivity for any constant number of rounds by extending deterministic lower bounds shown by Ponzio, Radhakrishnan and Venkatesh (JCSS 2001) to the randomized setting.
Cite as

Jaikumar Radhakrishnan, Chaitanya Reddy, and Rakesh Venkat. Optimal Two-Round Communication Lower Bound for Graph Connectivity via Pointer Chasing. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 110:1-110:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{radhakrishnan_et_al:LIPIcs.ITCS.2026.110,
  author =	{Radhakrishnan, Jaikumar and Reddy, Chaitanya and Venkat, Rakesh},
  title =	{{Optimal Two-Round Communication Lower Bound for Graph Connectivity via Pointer Chasing}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{110:1--110:20},
  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.2026.110},
  URN =		{urn:nbn:de:0030-drops-253974},
  doi =		{10.4230/LIPIcs.ITCS.2026.110},
  annote =	{Keywords: Communication complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.112
Lower Bounds Beyond DNF of Parities

Authors: Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov

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

Abstract
We consider a subclass of AC⁰[2] circuits that simultaneously captures DNF∘Xor and depth-3 AC⁰ circuits. For this class we show a technique for proving lower bounds inspired by the top-down approach. We give lower bounds for the middle slice function, inner product function, and affine dispersers.
Cite as

Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov. Lower Bounds Beyond DNF of Parities. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{riazanov_et_al:LIPIcs.ITCS.2026.112,
  author =	{Riazanov, Artur and Sofronova, Anastasia and Sokolov, Dmitry},
  title =	{{Lower Bounds Beyond DNF of Parities}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{112:1--112:15},
  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.2026.112},
  URN =		{urn:nbn:de:0030-drops-253996},
  doi =		{10.4230/LIPIcs.ITCS.2026.112},
  annote =	{Keywords: boolean circuits, top-down, unpredictability}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.55
Lifting to Randomized Parity Decision Trees

Authors: Farzan Byramji and Russell Impagliazzo

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

Abstract
We prove a lifting theorem from randomized decision tree depth to randomized parity decision tree (PDT) size. We use the same property of the gadget, stifling, which was introduced by Chattopadhyay, Mande, Sanyal and Sherif [ITCS 23] to prove a lifting theorem for deterministic PDTs. Moreover, even the milder condition that the gadget has minimum parity certificate complexity at least 2 suffices for lifting to randomized PDT size. To improve the dependence on the gadget g in the lower bounds for composed functions, we consider a related problem g_* whose inputs are certificates of g. It is implicit in the work of Chattopadhyay et al. that for any function f, lower bounds for the *-depth of f_* give lower bounds for the PDT size of f. We make this connection explicit in the deterministic case and show that it also holds for randomized PDTs. We then combine this with composition theorems for *-depth, which follow by adapting known composition theorems for decision trees. As a corollary, we get tight lifting theorems when the gadget is Indexing, Inner Product or Disjointness.
Cite as

Farzan Byramji and Russell Impagliazzo. Lifting to Randomized Parity Decision Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 55:1-55:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{byramji_et_al:LIPIcs.APPROX/RANDOM.2025.55,
  author =	{Byramji, Farzan and Impagliazzo, Russell},
  title =	{{Lifting to Randomized Parity Decision Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{55:1--55:22},
  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.2025.55},
  URN =		{urn:nbn:de:0030-drops-244213},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.55},
  annote =	{Keywords: Parity decision trees, composition}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.64
Searching for Falsified Clause in Random (log{n})-CNFs Is Hard for Randomized Communication

Authors: Artur Riazanov, Anastasia Sofronova, Dmitry Sokolov, and Weiqiang Yuan

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

Abstract
We show that for a randomly sampled unsatisfiable O(log n)-CNF over n variables the randomized two-party communication cost of finding a clause falsified by the given variable assignment is linear in n.
Cite as

Artur Riazanov, Anastasia Sofronova, Dmitry Sokolov, and Weiqiang Yuan. Searching for Falsified Clause in Random (log{n})-CNFs Is Hard for Randomized Communication. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 64:1-64:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{riazanov_et_al:LIPIcs.APPROX/RANDOM.2025.64,
  author =	{Riazanov, Artur and Sofronova, Anastasia and Sokolov, Dmitry and Yuan, Weiqiang},
  title =	{{Searching for Falsified Clause in Random (log\{n\})-CNFs Is Hard for Randomized Communication}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{64:1--64:17},
  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.2025.64},
  URN =		{urn:nbn:de:0030-drops-244306},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.64},
  annote =	{Keywords: communication complexity, proof complexity, random CNF}
}
Document
DOI: 10.4230/LIPIcs.ITC.2025.12
Key-Agreement with Perfect Completeness from Random Oracles

Authors: Noam Mazor

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract
In the Random Oracle Model (ROM) all parties have oracle access to a common random function, and the parties are limited in the number of queries they can make to the oracle. The Merkle’s Puzzles protocol, introduced by Merkle [CACM '78], is a key-agreement protocol in the ROM with a quadratic gap between the query complexity of the honest parties and the eavesdropper. This quadratic gap is known to be optimal, by the works of Impagliazzo and Rudich [STOC ’89] and Barak and Mahmoody [Crypto ’09]. When the oracle function is injective or a permutation, Merkle’s Puzzles has perfect completeness. That is, it is certain that the protocol results in agreement between the parties. However, without such an assumption on the random function, there is a small error probability, and the parties may end up holding different keys. This fact raises the question: Is there a key-agreement protocol with perfect completeness and super-linear security in the ROM? In this paper we give a positive answer to the above question, showing that changes to the query distribution of the parties in Merkle’s Puzzles, yield a protocol with perfect completeness and roughly the same security.
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Noam Mazor. Key-Agreement with Perfect Completeness from Random Oracles. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 12:1-12:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mazor:LIPIcs.ITC.2025.12,
  author =	{Mazor, Noam},
  title =	{{Key-Agreement with Perfect Completeness from Random Oracles}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{12:1--12:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.12},
  URN =		{urn:nbn:de:0030-drops-243628},
  doi =		{10.4230/LIPIcs.ITC.2025.12},
  annote =	{Keywords: Key-Agreement, Random Oracle, Merkle’s Puzzles, Perfect Completeness}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.33
A Min-Entropy Approach to Multi-Party Communication Lower Bounds

Authors: Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang

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

Abstract
Information complexity is one of the most powerful techniques to prove information-theoretical lower bounds, in which Shannon entropy plays a central role. Though Shannon entropy has some convenient properties, such as the chain rule, it still has inherent limitations. One of the most notable barriers is the square-root loss, which appears in the square-root gap between entropy gaps and statistical distances, e.g., Pinsker’s inequality. To bypass this barrier, we introduce a new method based on min-entropy analysis. Building on this new method, we prove the following results. - An Ω(N^{∑_i α_i - max_i {α_i}}/k) randomized communication lower bound of the k-party set-intersection problem where the i-th party holds a random set of size ≈ N^{1-α_i}. - A tight Ω(n/k) randomized lower bound of the k-party Tree Pointer Jumping problems, improving an Ω(n/k²) lower bound by Chakrabarti, Cormode, and McGregor (STOC 08). - An Ω(n/k+√n) lower bound of the Chained Index problem, improving an Ω(n/k²) lower bound by Cormode, Dark, and Konrad (ICALP 19). Since these problems served as hard problems for numerous applications in streaming lower bounds and cryptography, our new lower bounds directly improve these streaming lower bounds and cryptography lower bounds. On the technical side, min-entropy does not have nice properties such as the chain rule. To address this issue, we enhance the structure-vs-pseudorandomness decomposition used by Göös, Pitassi, and Watson (FOCS 17) and Yang and Zhang (STOC 24); both papers used this decomposition to prove communication lower bounds. In this paper, we give a new breath to this method in the multi-party setting, presenting a new toolkit for proving multi-party communication lower bounds.
Cite as

Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang. A Min-Entropy Approach to Multi-Party Communication Lower Bounds. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 33:1-33:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.CCC.2025.33,
  author =	{Huang, Mi-Ying (Miryam) and Mao, Xinyu and Wang, Shuo and Yang, Guangxu and Zhang, Jiapeng},
  title =	{{A Min-Entropy Approach to Multi-Party Communication Lower Bounds}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{33:1--33:29},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-237273},
  doi =		{10.4230/LIPIcs.CCC.2025.33},
  annote =	{Keywords: communication complexity, lifting theorems, set intersection, chained index}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.4
Hardness of Clique Approximation for Monotone Circuits

Authors: Jarosław Błasiok and Linus Meierhöfer

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

Abstract
We consider a problem of approximating the size of the largest clique in a graph, using a monotone circuit. Concretely, we focus on distinguishing a random Erdős–Rényi graph 𝒢_{n,p}, with p = n^{-2/(α-1)} chosen st. with high probability it does not even contain an α-clique, from a random clique on β vertices (where α ≤ β). Using the approximation method of Razborov, Alon and Boppana showed in their influential work in 1987 that as long as √{α} β < n^{1-δ}/log n, this problem requires a monotone circuit of size n^Ω(δ√α), implying a lower bound of 2^Ω̃(n^{1/3}) for the exact version of the problem Clique_k when k≈ n^{2/3}. Recently, Cavalar, Kumar, and Rossman improved their result by showing a tight lower bound n^Ω(k), in a limited range k ≤ n^{1/3}, implying a comparable 2^Ω̃(n^{1/3}) lower bound after choosing the largest admissible k. We combine the ideas of Cavalar, Kumar and Rossman with recent breakthrough results on sunflower conjecture by Alweiss, Lovett, Wu, and Zhang to show that as long as α β < n^{1-δ}/log n, any monotone circuit rejecting 𝒢_{n,p} graph while accepting a β-clique needs to have size at least n^Ω(δ²α); this implies a stronger 2^Ω̃(√n) lower bound for the unrestricted version of the problem. We complement this result with a construction of an explicit monotone circuit of size O(n^{δ² α/2}) which rejects 𝒢_{n,p}, and accepts any graph containing β-clique whenever β > n^{1-δ}. In particular, those two theorems give a precise characterization of the smallest β-clique that can be distinguished from 𝒢_{n, 1/2}: when β > n / 2^{C √{log n}}, there is a polynomial-size circuit that solves it, while for β < n / 2^ω(√{log n}) every circuit needs size n^ω(1).
Cite as

Jarosław Błasiok and Linus Meierhöfer. Hardness of Clique Approximation for Monotone Circuits. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blasiok_et_al:LIPIcs.CCC.2025.4,
  author =	{B{\l}asiok, Jaros{\l}aw and Meierh\"{o}fer, Linus},
  title =	{{Hardness of Clique Approximation for Monotone Circuits}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{4:1--4:20},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-236987},
  doi =		{10.4230/LIPIcs.CCC.2025.4},
  annote =	{Keywords: circuit lower bounds, monotone circuits, sunflower conjecture}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.36
Lifting with Colourful Sunflowers

Authors: Susanna F. de Rezende and Marc Vinyals

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

Abstract
We show that a generalization of the DAG-like query-to-communication lifting theorem, when proven using sunflowers over non-binary alphabets, yields lower bounds on the monotone circuit complexity and proof complexity of natural functions and formulas that are better than previously known results obtained using the approximation method. These include an n^Ω(k) lower bound for the clique function up to k ≤ n^{1/2-ε}, and an exp(Ω(n^{1/3-ε})) lower bound for a function in P.
Cite as

Susanna F. de Rezende and Marc Vinyals. Lifting with Colourful Sunflowers. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{derezende_et_al:LIPIcs.CCC.2025.36,
  author =	{de Rezende, Susanna F. and Vinyals, Marc},
  title =	{{Lifting with Colourful Sunflowers}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{36:1--36:19},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-237303},
  doi =		{10.4230/LIPIcs.CCC.2025.36},
  annote =	{Keywords: lifting, sunflower, clique, colouring, monotone circuit, cutting planes}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.21
Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles

Authors: Paul Beame and Michael Whitmeyer

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

Abstract
We prove several results concerning the communication complexity of a collision-finding problem, each of which has applications to the complexity of cutting-plane proofs, which make inferences based on integer linear inequalities. In particular, we prove an Ω(n^{1-1/k} log k /2^k) lower bound on the k-party number-in-hand communication complexity of collision-finding. This implies a 2^{n^{1-o(1)}} lower bound on the size of tree-like cutting-planes refutations of the bit pigeonhole principle CNFs, which are compact and natural propositional encodings of the negation of the pigeonhole principle, improving on the best previous lower bound of 2^{Ω(√n)}. Using the method of density-restoring partitions, we also extend that previous lower bound to the full range of pigeonhole parameters. Finally, using a refinement of a bottleneck-counting framework of Haken and Cook and Sokolov for DAG-like communication protocols, we give a 2^{Ω(n^{1/4})} lower bound on the size of fully general (not necessarily tree-like) cutting planes refutations of the same bit pigeonhole principle formulas, improving on the best previous lower bound of 2^{Ω(n^{1/8})}.
Cite as

Paul Beame and Michael Whitmeyer. Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beame_et_al:LIPIcs.ICALP.2025.21,
  author =	{Beame, Paul and Whitmeyer, Michael},
  title =	{{Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.21},
  URN =		{urn:nbn:de:0030-drops-233982},
  doi =		{10.4230/LIPIcs.ICALP.2025.21},
  annote =	{Keywords: Proof Complexity, Communication Complexity}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2025.4
Some Recent Advancements in Monotone Circuit Complexity (Invited Talk)

Authors: Susanna F. de Rezende

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

Abstract
In 1985, Razborov [Razborov, 1985] proved the first superpolynomial size lower bound for monotone Boolean circuits for the perfect matching the clique functions, and, independently, Andreev [Andreev, 1985] obtained exponential size lower bounds. These breakthroughs were soon followed by further advancements in monotone complexity, including better lower bounds for clique [Alon and Boppana, 1987; Ingo Wegener, 1987], superlogarithmic depth lower bounds for connectivity by Karchmer and Wigderson [Karchmer and Wigderson, 1990], and the separations mon-NC ≠ mon-P and that mon-NC^i ≠ mon-NC^{i+1} by Raz and McKenzie [Ran Raz and Pierre McKenzie, 1999]. Karchmer and Wigderson [Karchmer and Wigderson, 1990] proved their result by establishing a relation between communication complexity and (monotone) circuit depth, and Raz and McKenzie [Ran Raz and Pierre McKenzie, 1999] introduced a new technique, now called lifting theorems, for obtaining communication lower bounds from query complexity lower bounds, In this talk, we will survey recent advancements in monotone complexity driven by query-to-communication lifting theorems. A decade ago, Göös, Pitassi, and Watson [Mika Göös et al., 2018] brought to light the generality of the result of Raz and McKenzie [Ran Raz and Pierre McKenzie, 1999] and reignited this line of work. A notable extension is the lifting theorem [Ankit Garg et al., 2020] for a model of DAG-like communication [Alexander A. Razborov, 1995; Dmitry Sokolov, 2017] that corresponds to circuit size. These powerful theorems, in their different flavours, have been instrumental in addressing many open questions in monotone circuit complexity, including: optimal 2^Ω(n) lower bounds on the size of monotone Boolean formulas computing an explicit function in NP [Toniann Pitassi and Robert Robere, 2017]; a complete picture of the relation between the mon-AC and mon-NC hierarchies [Susanna F. de Rezende et al., 2016]; a near optimal separation between monotone circuit and monotone formula size [Susanna F. de Rezende et al., 2020]; exponential separation between NC^2 and mon-P [Ankit Garg et al., 2020; Mika Göös et al., 2019]; and better lower bounds for clique [de Rezende and Vinyals, 2025; Lovett et al., 2022], improving on [Cavalar et al., 2021]. Very recently, lifting theorems were also used to prove supercritical trade-offs for monotone circuits showing that there are functions computable by small circuits for which any small circuit must have superlinear or even superpolynomial depth [de Rezende et al., 2024; Göös et al., 2024]. We will explore these results and their implications, and conclude by discussing some open problems.
Cite as

Susanna F. de Rezende. Some Recent Advancements in Monotone Circuit Complexity (Invited Talk). In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 4:1-4:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{derezende:LIPIcs.STACS.2025.4,
  author =	{de Rezende, Susanna F.},
  title =	{{Some Recent Advancements in Monotone Circuit Complexity}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{4:1--4:2},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-228291},
  doi =		{10.4230/LIPIcs.STACS.2025.4},
  annote =	{Keywords: monotone circuit complexity, query complexity, lifting theorems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.89
Optimal Communication Complexity of Chained Index

Authors: Janani Sundaresan

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

Abstract
We study the chain communication problem introduced by Cormode et al. [ICALP 2019]. For k ≥ 1, in the chain_{n,k} problem, there are k string and index pairs (X_i, σ_i) for i ∈ [k] such that the value at position σ_i in string X_i is the same bit for all k pairs. The input is shared between k+1 players as follows. Player 1 has the first string X₁ ∈ {0,1}ⁿ, player 2 has the first index σ₁ ∈ [n] and the second string X₂ ∈ {0,1}ⁿ, player 3 has the second index σ₂ ∈ [n] along with the third string X₃ ∈ {0,1}ⁿ, and so on. Player k+1 has the last index σ_k ∈ [n]. The communication is one way from each player to the next, starting from player 1 to player 2, then from player 2 to player 3 and so on. Player k+1, after receiving the message from player k, has to output a single bit which is the value at position σ_i in X_i for any i ∈ [k]. It is a generalization of the well-studied index problem, which is equivalent to chain_{n, 2}. Cormode et al. proved that the chain_{n,k} problem requires Ω(n/k²) communication, and they used it to prove streaming lower bounds for the approximation of maximum independent sets. Subsequently, Feldman et al. [STOC 2020] used it to prove lower bounds for streaming submodular maximization. However, it is not known whether the Ω(n/k²) lower bound used in these works is optimal for the problem, and in fact, it was conjectured by Cormode et al. that Ω(n) bits are necessary. We prove the optimal lower bound of Ω(n) for chain_{n,k} when k = o(n/log n) as our main result. This settles the open conjecture of Cormode et al., barring the range of k = Ω(n /log n). The main technique is a reduction to a non-standard index problem where the input to the players is such that the answer is biased away from uniform. This biased version of index is analyzed using tools from information theory. As a corollary, we get an improved lower bound for approximation of maximum independent set in vertex arrival streams via a reduction from chain directly.
Cite as

Janani Sundaresan. Optimal Communication Complexity of Chained Index. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 89:1-89:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sundaresan:LIPIcs.ITCS.2025.89,
  author =	{Sundaresan, Janani},
  title =	{{Optimal Communication Complexity of Chained Index}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{89:1--89:18},
  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.2025.89},
  URN =		{urn:nbn:de:0030-drops-227172},
  doi =		{10.4230/LIPIcs.ITCS.2025.89},
  annote =	{Keywords: communication complexity, index communciation problem}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.78
Randomized Lifting to Semi-Structured Communication Complexity via Linear Diversity

Authors: Vladimir Podolskii and Alexander Shekhovtsov

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

Abstract
We study query-to-communication lifting. The major open problem in this area is to prove a lifting theorem for gadgets of constant size. The recent paper [Paul Beame and Sajin Koroth, 2023] introduces semi-structured communication complexity, in which one of the players can only send parities of their input bits. They have shown that for any m ≥ 4 deterministic decision tree complexity of a function f can be lifted to the so called semi-structured communication complexity of f∘Ind_m, where Ind_m is the Indexing gadget. As our main contribution we extend these results to randomized setting. Our results also apply to a substantially larger set of gadgets. More specifically, we introduce a new complexity measure of gadgets, linear diversity. For all gadgets g with non-trivial linear diversity we show that randomized decision tree complexity of f lifts to randomized semi-structured communication complexity of f∘g. In particular, this gives tight lifting results for Indexing gadget Ind_m, Inner Product gadget IP_m for all m ≥ 2, and for Majority gadget MAJ_m for all m ≥ 4. We prove the same results for deterministic case. From our result it immediately follows that deterministic/randomized decision tree complexity lifts to deterministic/randomized parity decision tree complexity. For randomized case this is the first result of this type. For deterministic case, our result improves the bound in [Arkadev Chattopadhyay et al., 2023] for Inner Product gadget. To obtain our results we introduce a new secret sets approach to simulation of semi-structured communication protocols by decision trees. It allows us to simulate (restricted classes of) communication protocols on truly uniform distribution of inputs.
Cite as

Vladimir Podolskii and Alexander Shekhovtsov. Randomized Lifting to Semi-Structured Communication Complexity via Linear Diversity. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 78:1-78:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{podolskii_et_al:LIPIcs.ITCS.2025.78,
  author =	{Podolskii, Vladimir and Shekhovtsov, Alexander},
  title =	{{Randomized Lifting to Semi-Structured Communication Complexity via Linear Diversity}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{78:1--78:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.78},
  URN =		{urn:nbn:de:0030-drops-227061},
  doi =		{10.4230/LIPIcs.ITCS.2025.78},
  annote =	{Keywords: communication complexity, decision trees, lifting}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.17
Random Restrictions of Bounded Low Degree Polynomials Are Juntas

Authors: Sreejata Kishor Bhattacharya

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

Abstract
We study the effects of random restrictions on low degree functions that are bounded on every point of the Boolean cube. Our main result shows that, with high probability, the restricted function can be approximated by a junta of arity that is just polynomial in the original degree. More precisely, let f: {± 1}ⁿ → [0,1] be a degree d polynomial (d ≥ 2) and let ρ denote a random restriction with survival probability O(log(d)/d). Then, with probability at least 1-d^{-Ω(1)}, there exists a function g: {± 1}ⁿ → [0,1] depending on at most d^O(1) coordinates such that ||f_{ρ}-g||_2^2 ≤ d^{-1-Ω(1)}. Our result has the following consequence for the well known, outstanding conjecture of Aaronson and Ambainis. The Aaronson-Ambainis conjecture was formulated to show that the acceptance probability of a quantum query algorithm can be well approximated almost everywhere by a classical query algorithm with a polynomial blow-up: it speculates that a polynomal f: {± 1}ⁿ → [0,1] with degree d has a coordinate with influence ≥ poly(1/d, Var[f]). Our result shows that this is true for a non-negligible fraction of random restrictions of f assuming Var[f] is not too low. Our work combines the ideas of Dinur, Friedgut, Kindler and O'Donnell [Dinur et al., 2006] with an approximation theoretic result, first reported in the recent work of Filmus, Hatami, Keller and Lifshitz [Yuval Filmus and Hamed Hatami, 2014].
Cite as

Sreejata Kishor Bhattacharya. Random Restrictions of Bounded Low Degree Polynomials Are Juntas. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhattacharya:LIPIcs.ITCS.2025.17,
  author =	{Bhattacharya, Sreejata Kishor},
  title =	{{Random Restrictions of Bounded Low Degree Polynomials Are Juntas}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{17:1--17:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.17},
  URN =		{urn:nbn:de:0030-drops-226459},
  doi =		{10.4230/LIPIcs.ITCS.2025.17},
  annote =	{Keywords: Analysis of Boolean Functions, Quantum Query Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.75
Gadgetless Lifting Beats Round Elimination: Improved Lower Bounds for Pointer Chasing

Authors: Xinyu Mao, Guangxu Yang, and Jiapeng Zhang

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

Abstract
We prove an Ω(n / k + k) communication lower bound on (k - 1)-round distributional complexity of the k-step pointer chasing problem under uniform input distribution, improving the Ω(n/k - klog n) lower bound due to Yehudayoff (Combinatorics Probability and Computing, 2020). Our lower bound almost matches the upper bound of Õ(n/k + k) communication by Nisan and Wigderson (STOC 91). As part of our approach, we put forth gadgetless lifting, a new framework that lifts lower bounds for a family of restricted protocols into lower bounds for general protocols. A key step in gadgetless lifting is choosing the appropriate definition of restricted protocols. In this paper, our definition of restricted protocols is inspired by the structure-vs-pseudorandomness decomposition by Göös, Pitassi, and Watson (FOCS 17) and Yang and Zhang (STOC 24). Previously, round-communication trade-offs were mainly obtained by round elimination and information complexity. Both methods have some barriers in some situations, and we believe gadgetless lifting could potentially address these barriers.
Cite as

Xinyu Mao, Guangxu Yang, and Jiapeng Zhang. Gadgetless Lifting Beats Round Elimination: Improved Lower Bounds for Pointer Chasing. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 75:1-75:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mao_et_al:LIPIcs.ITCS.2025.75,
  author =	{Mao, Xinyu and Yang, Guangxu and Zhang, Jiapeng},
  title =	{{Gadgetless Lifting Beats Round Elimination: Improved Lower Bounds for Pointer Chasing}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{75:1--75:14},
  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.2025.75},
  URN =		{urn:nbn:de:0030-drops-227038},
  doi =		{10.4230/LIPIcs.ITCS.2025.75},
  annote =	{Keywords: communication complexity, lifting theorems, pointer chasing}
}
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