4 Search Results for "He, William"

Document
DOI: 10.4230/LIPIcs.CCC.2023.22
A Distribution Testing Oracle Separating QMA and QCMA

Authors: Anand Natarajan and Chinmay Nirkhe

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
It is a long-standing open question in quantum complexity theory whether the definition of non-deterministic quantum computation requires quantum witnesses (QMA) or if classical witnesses suffice (QCMA). We make progress on this question by constructing a randomized classical oracle separating the respective computational complexity classes. Previous separations [Aaronson and Kuperberg, 2007; Bill Fefferman and Shelby Kimmel, 2018] required a quantum unitary oracle. The separating problem is deciding whether a distribution supported on regular un-directed graphs either consists of multiple connected components (yes instances) or consists of one expanding connected component (no instances) where the graph is given in an adjacency-list format by the oracle. Therefore, the oracle is a distribution over n-bit boolean functions.
Cite as

Anand Natarajan and Chinmay Nirkhe. A Distribution Testing Oracle Separating QMA and QCMA. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 22:1-22:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{natarajan_et_al:LIPIcs.CCC.2023.22,
  author =	{Natarajan, Anand and Nirkhe, Chinmay},
  title =	{{A Distribution Testing Oracle Separating QMA and QCMA}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{22:1--22:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.22},
  URN =		{urn:nbn:de:0030-drops-182928},
  doi =		{10.4230/LIPIcs.CCC.2023.22},
  annote =	{Keywords: quantum non-determinism, complexity theory}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.11
Minimum-Membership Geometric Set Cover, Revisited

Authors: Sayan Bandyapadhyay, William Lochet, Saket Saurabh, and Jie Xue

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We revisit a natural variant of the geometric set cover problem, called minimum-membership geometric set cover (MMGSC). In this problem, the input consists of a set S of points and a set ℛ of geometric objects, and the goal is to find a subset ℛ^* ⊆ ℛ to cover all points in S such that the membership of S with respect to ℛ^*, denoted by memb(S,ℛ^*), is minimized, where memb(S,ℛ^*) = max_{p ∈ S} |{R ∈ ℛ^*: p ∈ R}|. We give the first polynomial-time approximation algorithms for MMGSC in ℝ². Specifically, we achieve the following two main results. - We give the first polynomial-time constant-approximation algorithm for MMGSC with unit squares. This answers a question left open since the work of Erlebach and Leeuwen [SODA'08], who gave a constant-approximation algorithm with running time n^{O(opt)} where opt is the optimum of the problem (i.e., the minimum membership). - We give the first polynomial-time approximation scheme (PTAS) for MMGSC with halfplanes. Prior to this work, it was even unknown whether the problem can be approximated with a factor of o(log n) in polynomial time, while it is well-known that the minimum-size set cover problem with halfplanes can be solved in polynomial time. We also consider a problem closely related to MMGSC, called minimum-ply geometric set cover (MPGSC), in which the goal is to find ℛ^* ⊆ ℛ to cover S such that the ply of ℛ^* is minimized, where the ply is defined as the maximum number of objects in ℛ^* which have a nonempty common intersection. Very recently, Durocher et al. gave the first constant-approximation algorithm for MPGSC with unit squares which runs in O(n^{12}) time. We give a significantly simpler constant-approximation algorithm with near-linear running time.
Cite as

Sayan Bandyapadhyay, William Lochet, Saket Saurabh, and Jie Xue. Minimum-Membership Geometric Set Cover, Revisited. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.SoCG.2023.11,
  author =	{Bandyapadhyay, Sayan and Lochet, William and Saurabh, Saket and Xue, Jie},
  title =	{{Minimum-Membership Geometric Set Cover, Revisited}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.11},
  URN =		{urn:nbn:de:0030-drops-178610},
  doi =		{10.4230/LIPIcs.SoCG.2023.11},
  annote =	{Keywords: geometric set cover, geometric optimization, approximation algorithms}
}
Document
DOI: 10.4230/OASIcs.EVCS.2023.3
Injecting Language Workbench Technology into Mainstream Languages

Authors: Michael Ballantyne and Matthias Felleisen

Published in: OASIcs, Volume 109, Eelco Visser Commemorative Symposium (EVCS 2023)

Abstract
Eelco Visser envisioned a future where DSLs become a commonplace abstraction in software development. He took strides towards implementing this vision with the Spoofax language workbench. However, his vision is far from the mainstream of programming today. How will the many mainstream programmers encounter and adopt language workbench technology? We propose that the macro systems found in emerging industrial languages open a path towards delivering language workbenches as easy-to-adopt libraries. To develop the idea, we sketch an implementation of a language workbench as a macro-library atop Racket and identify the key features of the macro system needed to enable this evolution path.
Cite as

Michael Ballantyne and Matthias Felleisen. Injecting Language Workbench Technology into Mainstream Languages. In Eelco Visser Commemorative Symposium (EVCS 2023). Open Access Series in Informatics (OASIcs), Volume 109, pp. 3:1-3:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ballantyne_et_al:OASIcs.EVCS.2023.3,
  author =	{Ballantyne, Michael and Felleisen, Matthias},
  title =	{{Injecting Language Workbench Technology into Mainstream Languages}},
  booktitle =	{Eelco Visser Commemorative Symposium (EVCS 2023)},
  pages =	{3:1--3:11},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-267-9},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{109},
  editor =	{L\"{a}mmel, Ralf and Mosses, Peter D. and Steimann, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.EVCS.2023.3},
  URN =		{urn:nbn:de:0030-drops-177737},
  doi =		{10.4230/OASIcs.EVCS.2023.3},
  annote =	{Keywords: Language workbenches, macro systems, language adoption}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.68
Symmetric Formulas for Products of Permutations

Authors: William He and Benjamin Rossman

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

Abstract
We study the formula complexity of the word problem Word_{S_n,k} : {0,1}^{kn²} → {0,1}: given n-by-n permutation matrices M₁,… ,M_k, compute the (1,1)-entry of the matrix product M₁⋯ M_k. An important feature of this function is that it is invariant under action of S_n^{k-1} given by (π₁,… ,π_{k-1})(M₁,… ,M_k) = (M₁π₁^{-1},π₁M₂π₂^{-1},… ,π_{k-2}M_{k-1}π_{k-1}^{-1},π_{k-1}M_k). This symmetry is also exhibited in the smallest known unbounded fan-in {and,or,not}-formulas for Word_{S_n,k}, which have size n^O(log k). In this paper we prove a matching n^{Ω(log k)} lower bound for S_n^{k-1}-invariant formulas computing Word_{S_n,k}. This result is motivated by the fact that a similar lower bound for unrestricted (non-invariant) formulas would separate complexity classes NC¹ and Logspace. Our more general main theorem gives a nearly tight n^d(k^{1/d}-1) lower bound on the G^{k-1}-invariant depth-d {maj,and,or,not}-formula size of Word_{G,k} for any finite simple group G whose minimum permutation representation has degree n. We also give nearly tight lower bounds on the G^{k-1}-invariant depth-d {and,or,not}-formula size in the case where G is an abelian group.
Cite as

William He and Benjamin Rossman. Symmetric Formulas for Products of Permutations. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 68:1-68:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{he_et_al:LIPIcs.ITCS.2023.68,
  author =	{He, William and Rossman, Benjamin},
  title =	{{Symmetric Formulas for Products of Permutations}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{68:1--68:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.68},
  URN =		{urn:nbn:de:0030-drops-175717},
  doi =		{10.4230/LIPIcs.ITCS.2023.68},
  annote =	{Keywords: circuit complexity, group-invariant formulas}
}
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