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Documents authored by Qi, Qi


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Qi, Qi

Document
Understanding PPA-Completeness

Authors: Xiaotie Deng, Jack R. Edmonds, Zhe Feng, Zhengyang Liu, Qi Qi, and Zeying Xu

Published in: LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)


Abstract
We consider the problem of finding a fully colored base triangle on the 2-dimensional Möbius band under the standard boundary condition, proving it to be PPA-complete. The proof is based on a construction for the DPZP problem, that of finding a zero point under a discrete version of continuity condition. It further derives PPA-completeness for versions on the Möbius band of other related discrete fixed point type problems, and a special version of the Tucker problem, finding an edge such that if the value of one end vertex is x, the other is -x, given a special anti-symmetry boundary condition. More generally, this applies to other non-orientable spaces, including the projective plane and the Klein bottle. However, since those models have a closed boundary, we rely on a version of the PPA that states it as to find another fixed point giving a fixed point. This model also makes it presentationally simple for an extension to a high dimensional discrete fixed point problem on a non-orientable (nearly) hyper-grid with a constant side length.

Cite as

Xiaotie Deng, Jack R. Edmonds, Zhe Feng, Zhengyang Liu, Qi Qi, and Zeying Xu. Understanding PPA-Completeness. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 23:1-23:25, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{deng_et_al:LIPIcs.CCC.2016.23,
  author =	{Deng, Xiaotie and Edmonds, Jack R. and Feng, Zhe and Liu, Zhengyang and Qi, Qi and Xu, Zeying},
  title =	{{Understanding PPA-Completeness}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{23:1--23:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Raz, Ran},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.23},
  URN =		{urn:nbn:de:0030-drops-58310},
  doi =		{10.4230/LIPIcs.CCC.2016.23},
  annote =	{Keywords: Fixed Point Computation, PPA-Completeness}
}

Qi, Xuanrui

Document
Proving Tree Algorithms for Succinct Data Structures

Authors: Reynald Affeldt, Jacques Garrigue, Xuanrui Qi, and Kazunari Tanaka

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)


Abstract
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely on cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect of two different tree-based succinct representations and their accompanying algorithms. One is the Level-Order Unary Degree Sequence, which encodes the structure of a tree in breadth-first order as a sequence of bits, where access operations can be defined in terms of Rank and Select, which work in constant time for static bit sequences. The other represents dynamic bit sequences as binary balanced trees, where Rank and Select present a low logarithmic overhead compared to their static versions, and with efficient insertion and deletion. The two can be stacked to provide a dynamic representation of dictionaries for instance. While both representations are well-known, we believe this to be their first formalization and a needed step towards provably-safe implementations of big data.

Cite as

Reynald Affeldt, Jacques Garrigue, Xuanrui Qi, and Kazunari Tanaka. Proving Tree Algorithms for Succinct Data Structures. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{affeldt_et_al:LIPIcs.ITP.2019.5,
  author =	{Affeldt, Reynald and Garrigue, Jacques and Qi, Xuanrui and Tanaka, Kazunari},
  title =	{{Proving Tree Algorithms for Succinct Data Structures}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.5},
  URN =		{urn:nbn:de:0030-drops-110609},
  doi =		{10.4230/LIPIcs.ITP.2019.5},
  annote =	{Keywords: Coq, small-scale reflection, succinct data structures, LOUDS, bit vectors, self balancing trees}
}
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