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Documents authored by Guan, Ziyi

Document
DOI: 10.4230/LIPIcs.STACS.2024.39
Quantum and Classical Communication Complexity of Permutation-Invariant Functions

Authors: Ziyi Guan, Yunqi Huang, Penghui Yao, and Zekun Ye

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
This paper gives a nearly tight characterization of the quantum communication complexity of the permutation-invariant Boolean functions. With such a characterization, we show that the quantum and randomized communication complexity of the permutation-invariant Boolean functions are quadratically equivalent (up to a logarithmic factor). Our results extend a recent line of research regarding query complexity [Scott Aaronson and Andris Ambainis, 2014; André Chailloux, 2019; Shalev Ben-David et al., 2020] to communication complexity, showing symmetry prevents exponential quantum speedups. Furthermore, we show the Log-rank Conjecture holds for any non-trivial total permutation-invariant Boolean function. Moreover, we establish a relationship between the quantum/classical communication complexity and the approximate rank of permutation-invariant Boolean functions. This implies the correctness of the Log-approximate-rank Conjecture for permutation-invariant Boolean functions in both randomized and quantum settings (up to a logarithmic factor).
Cite as

Ziyi Guan, Yunqi Huang, Penghui Yao, and Zekun Ye. Quantum and Classical Communication Complexity of Permutation-Invariant Functions. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{guan_et_al:LIPIcs.STACS.2024.39,
  author =	{Guan, Ziyi and Huang, Yunqi and Yao, Penghui and Ye, Zekun},
  title =	{{Quantum and Classical Communication Complexity of Permutation-Invariant Functions}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{39:1--39:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.39},
  URN =		{urn:nbn:de:0030-drops-197498},
  doi =		{10.4230/LIPIcs.STACS.2024.39},
  annote =	{Keywords: Communication complexity, Permutation-invariant functions, Log-rank Conjecture, Quantum advantages}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.34
On Parallel Repetition of PCPs

Authors: Alessandro Chiesa, Ziyi Guan, and Burcu Yıldız

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

Abstract
Parallel repetition refers to a set of valuable techniques used to reduce soundness error of probabilistic proofs while saving on certain efficiency measures. Parallel repetition has been studied for interactive proofs (IPs) and multi-prover interactive proofs (MIPs). In this paper we initiate the study of parallel repetition for probabilistically checkable proofs (PCPs). We show that, perhaps surprisingly, parallel repetition of a PCP can increase soundness error, in fact bringing the soundness error to one as the number of repetitions tends to infinity. This "failure" of parallel repetition is common: we find that it occurs for a wide class of natural PCPs for NP-complete languages. We explain this unexpected phenomenon by providing a characterization result: the parallel repetition of a PCP brings the soundness error to zero if and only if a certain "MIP projection" of the PCP has soundness error strictly less than one. We show that our characterization is tight via a suitable example. Moreover, for those cases where parallel repetition of a PCP does bring the soundness error to zero, the aforementioned connection to MIPs offers preliminary results on the rate of decay of the soundness error. Finally, we propose a simple variant of parallel repetition, called consistent parallel repetition (CPR), which has the same randomness complexity and query complexity as the plain variant of parallel repetition. We show that CPR brings the soundness error to zero for every PCP (with non-trivial soundness error). In fact, we show that CPR decreases the soundness error at an exponential rate in the repetition parameter.
Cite as

Alessandro Chiesa, Ziyi Guan, and Burcu Yıldız. On Parallel Repetition of PCPs. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 34:1-34:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chiesa_et_al:LIPIcs.ITCS.2024.34,
  author =	{Chiesa, Alessandro and Guan, Ziyi and Y{\i}ld{\i}z, Burcu},
  title =	{{On Parallel Repetition of PCPs}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{34:1--34:14},
  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.2024.34},
  URN =		{urn:nbn:de:0030-drops-195629},
  doi =		{10.4230/LIPIcs.ITCS.2024.34},
  annote =	{Keywords: probabilistically checkable proofs, parallel repetition}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.51
Depth-3 Circuits for Inner Product

Authors: Mika Göös, Ziyi Guan, and Tiberiu Mosnoi

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
What is the Σ₃²-circuit complexity (depth 3, bottom-fanin 2) of the 2n-bit inner product function? The complexity is known to be exponential 2^{α_n n} for some α_n = Ω(1). We show that the limiting constant α := lim sup α_n satisfies 0.847... ≤ α ≤ 0.965... . Determining α is one of the seemingly-simplest open problems about depth-3 circuits. The question was recently raised by Golovnev, Kulikov, and Williams (ITCS 2021) and Frankl, Gryaznov, and Talebanfard (ITCS 2022), who observed that α ∈ [0.5,1]. To obtain our improved bounds, we analyse a covering LP that captures the Σ₃²-complexity up to polynomial factors. In particular, our lower bound is proved by constructing a feasible solution to the dual LP.
Cite as

Mika Göös, Ziyi Guan, and Tiberiu Mosnoi. Depth-3 Circuits for Inner Product. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 51:1-51:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{goos_et_al:LIPIcs.MFCS.2023.51,
  author =	{G\"{o}\"{o}s, Mika and Guan, Ziyi and Mosnoi, Tiberiu},
  title =	{{Depth-3 Circuits for Inner Product}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{51:1--51:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.51},
  URN =		{urn:nbn:de:0030-drops-185856},
  doi =		{10.4230/LIPIcs.MFCS.2023.51},
  annote =	{Keywords: Circuit complexity, inner product}
}
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