14 Search Results for "Medyckyj-Scott, David"

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.2024.1
A Qubit, a Coin, and an Advice String Walk into a Relational Problem

Authors: Scott Aaronson, Harry Buhrman, and William Kretschmer

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

Abstract
Relational problems (those with many possible valid outputs) are different from decision problems, but it is easy to forget just how different. This paper initiates the study of FBQP/qpoly, the class of relational problems solvable in quantum polynomial-time with the help of polynomial-sized quantum advice, along with its analogues for deterministic and randomized computation (FP, FBPP) and advice (/poly, /rpoly). Our first result is that FBQP/qpoly ≠ FBQP/poly, unconditionally, with no oracle - a striking contrast with what we know about the analogous decision classes. The proof repurposes the separation between quantum and classical one-way communication complexities due to Bar-Yossef, Jayram, and Kerenidis. We discuss how this separation raises the prospect of near-term experiments to demonstrate "quantum information supremacy," a form of quantum supremacy that would not depend on unproved complexity assumptions. Our second result is that FBPP ̸ ⊂ FP/poly - that is, Adleman’s Theorem fails for relational problems - unless PSPACE ⊂ NP/poly. Our proof uses IP = PSPACE and time-bounded Kolmogorov complexity. On the other hand, we show that proving FBPP ̸ ⊂ FP/poly will be hard, as it implies a superpolynomial circuit lower bound for PromiseBPEXP. We prove the following further results: - Unconditionally, FP ≠ FBPP and FP/poly ≠ FBPP/poly (even when these classes are carefully defined). - FBPP/poly = FBPP/rpoly (and likewise for FBQP). For sampling problems, by contrast, SampBPP/poly ≠ SampBPP/rpoly (and likewise for SampBQP).
Cite as

Scott Aaronson, Harry Buhrman, and William Kretschmer. A Qubit, a Coin, and an Advice String Walk into a Relational Problem. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{aaronson_et_al:LIPIcs.ITCS.2024.1,
  author =	{Aaronson, Scott and Buhrman, Harry and Kretschmer, William},
  title =	{{A Qubit, a Coin, and an Advice String Walk into a Relational Problem}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{1:1--1:24},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.1},
  URN =		{urn:nbn:de:0030-drops-195290},
  doi =		{10.4230/LIPIcs.ITCS.2024.1},
  annote =	{Keywords: Relational problems, quantum advice, randomized advice, FBQP, FBPP}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.51
An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets

Authors: Rafael Frongillo, Maneesha Papireddygari, and Bo Waggoner

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

Abstract
Constant-function market makers (CFMMs), such as Uniswap, are automated exchanges offering trades among a set of assets. We study their technical relationship to another class of automated market makers, cost-function prediction markets. We first introduce axioms for market makers and show that CFMMs with concave potential functions characterize "good" market makers according to these axioms. We then show that every such CFMM on n assets is equivalent to a cost-function prediction market for events with n outcomes. Our construction directly converts a CFMM into a prediction market, and vice versa. Using this equivalence, we give another construction which can produce any 1-homogenous, increasing, and concave CFMM, as are typically used in practice, from a cost function. Conceptually, our results show that desirable market-making axioms are equivalent to desirable information-elicitation axioms, i.e., markets are good at facilitating trade if and only if they are good at revealing beliefs. For example, we show that every CFMM implicitly defines a proper scoring rule for eliciting beliefs; the scoring rule for Uniswap is unusual, but known. From a technical standpoint, our results show how tools for prediction markets and CFMMs can interoperate. We illustrate this interoperability by showing how liquidity strategies from both literatures transfer to the other, yielding new market designs.
Cite as

Rafael Frongillo, Maneesha Papireddygari, and Bo Waggoner. An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{frongillo_et_al:LIPIcs.ITCS.2024.51,
  author =	{Frongillo, Rafael and Papireddygari, Maneesha and Waggoner, Bo},
  title =	{{An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{51:1--51:21},
  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.2024.51},
  URN =		{urn:nbn:de:0030-drops-195795},
  doi =		{10.4230/LIPIcs.ITCS.2024.51},
  annote =	{Keywords: Convex analysis, Equivalence result, Axiomatic characterization, Market Makers, Prediction markets, Scoring rules, Cost-functions}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.55
On the Fine-Grained Query Complexity of Symmetric Functions

Authors: Supartha Podder, Penghui Yao, and Zekun Ye

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
Watrous conjectured that the randomized and quantum query complexities of symmetric functions are polynomially equivalent, which was resolved by Ambainis and Aaronson [Scott Aaronson and Andris Ambainis, 2014], and was later improved in [André Chailloux, 2019; Shalev Ben-David et al., 2020]. This paper explores a fine-grained version of the Watrous conjecture, including the randomized and quantum algorithms with success probabilities arbitrarily close to 1/2. Our contributions include the following: 1) An analysis of the optimal success probability of quantum and randomized query algorithms of two fundamental partial symmetric Boolean functions given a fixed number of queries. We prove that for any quantum algorithm computing these two functions using T queries, there exist randomized algorithms using poly(T) queries that achieve the same success probability as the quantum algorithm, even if the success probability is arbitrarily close to 1/2. These two classes of functions are instrumental in analyzing general symmetric functions. 2) We establish that for any total symmetric Boolean function f, if a quantum algorithm uses T queries to compute f with success probability 1/2+β, then there exists a randomized algorithm using O(T²) queries to compute f with success probability 1/2 + Ω(δβ²) on a 1-δ fraction of inputs, where β,δ can be arbitrarily small positive values. As a corollary, we prove a randomized version of Aaronson-Ambainis Conjecture [Scott Aaronson and Andris Ambainis, 2014] for total symmetric Boolean functions in the regime where the success probability of algorithms can be arbitrarily close to 1/2. 3) We present polynomial equivalences for several fundamental complexity measures of partial symmetric Boolean functions. Specifically, we first prove that for certain partial symmetric Boolean functions, quantum query complexity is at most quadratic in approximate degree for any error arbitrarily close to 1/2. Next, we show exact quantum query complexity is at most quadratic in degree. Additionally, we give the tight bounds of several complexity measures, indicating their polynomial equivalence. Conversely, we exhibit an exponential separation between randomized and exact quantum query complexity for certain partial symmetric Boolean functions.
Cite as

Supartha Podder, Penghui Yao, and Zekun Ye. On the Fine-Grained Query Complexity of Symmetric Functions. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 55:1-55:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{podder_et_al:LIPIcs.ISAAC.2023.55,
  author =	{Podder, Supartha and Yao, Penghui and Ye, Zekun},
  title =	{{On the Fine-Grained Query Complexity of Symmetric Functions}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{55:1--55:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.55},
  URN =		{urn:nbn:de:0030-drops-193570},
  doi =		{10.4230/LIPIcs.ISAAC.2023.55},
  annote =	{Keywords: Query complexity, Symmetric functions, Quantum advantages}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2021.7
Twins: BFT Systems Made Robust

Authors: Shehar Bano, Alberto Sonnino, Andrey Chursin, Dmitri Perelman, Zekun Li, Avery Ching, and Dahlia Malkhi

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract
This paper presents Twins, an automated unit test generator of Byzantine attacks. Twins implements three types of Byzantine behaviors: (i) leader equivocation, (ii) double voting, and (iii) losing internal state such as forgetting "locks" guarding voted values. To emulate interesting attacks by a Byzantine node, it instantiates twin copies of the node instead of one, giving both twins the same identities and network credentials. To the rest of the system, the twins appear indistinguishable from a single node behaving in a "questionable" manner. Twins can systematically generate Byzantine attack scenarios at scale, execute them in a controlled manner, and examine their behavior. Twins scenarios iterate over protocol rounds and vary the communication patterns among nodes. Twins runs in a production setting within DiemBFT where it can execute 44M Twins-generated scenarios daily. Whereas the system at hand did not manifest errors, subtle safety bugs that were deliberately injected for the purpose of validating the implementation of Twins itself were exposed within minutes. Twins can prevent developers from regressing correctness when updating the codebase, introducing new features, or performing routine maintenance tasks. Twins only requires a thin wrapper over DiemBFT, we thus envision other systems using it. Building on this idea, one new attack and several known attacks against other BFT protocols were materialized as Twins scenarios. In all cases, the target protocols break within fewer than a dozen protocol rounds, hence it is realistic for the Twins approach to expose the problems.
Cite as

Shehar Bano, Alberto Sonnino, Andrey Chursin, Dmitri Perelman, Zekun Li, Avery Ching, and Dahlia Malkhi. Twins: BFT Systems Made Robust. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 7:1-7:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bano_et_al:LIPIcs.OPODIS.2021.7,
  author =	{Bano, Shehar and Sonnino, Alberto and Chursin, Andrey and Perelman, Dmitri and Li, Zekun and Ching, Avery and Malkhi, Dahlia},
  title =	{{Twins: BFT Systems Made Robust}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{7:1--7:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.7},
  URN =		{urn:nbn:de:0030-drops-157825},
  doi =		{10.4230/LIPIcs.OPODIS.2021.7},
  annote =	{Keywords: Distributed Systems, Byzantine Fault Tolerance, Real-World Deployment}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2021.II.13
Automated Georeferencing of Antarctic Species

Authors: Jamie Scott, Kristin Stock, Fraser Morgan, Brandon Whitehead, and David Medyckyj-Scott

Published in: LIPIcs, Volume 208, 11th International Conference on Geographic Information Science (GIScience 2021) - Part II

Abstract
Many text documents in the biological domain contain references to the toponym of specific phenomena (e.g. species sightings) in natural language form "In <LOCATION> Garwood Valley summer activity was 0.2% for <SPECIES> Umbilicaria aprina and 1.7% for <SPECIES> Caloplaca sp. ..." While methods have been developed to extract place names from documents, and attention has been given to the interpretation of spatial prepositions, the ability to connect toponym mentions in text with the phenomena to which they refer (in this case species) has been given limited attention, but would be of considerable benefit for the task of mapping specific phenomena mentioned in text documents. As part of work to create a pipeline to automate georeferencing of species within legacy documents, this paper proposes a method to: (1) recognise species and toponyms within text and (2) match each species mention to the relevant toponym mention. Our methods find significant promise in a bespoke rules- and dictionary-based approach to recognise species within text (F1 scores up to 0.87 including partial matches) but less success, as yet, recognising toponyms using multiple gazetteers combined with an off the shelf natural language processing tool (F1 up to 0.62). Most importantly, we offer a contribution to the relatively nascent area of matching toponym references to the object they locate (in our case species), including cases in which the toponym and species are in different sentences. We use tree-based models to achieve precision as high as 0.88 or an F1 score up to 0.68 depending on the downsampling rate. Initial results out perform previous research on detecting entity relationships that may cross sentence boundaries within biomedical text, and differ from previous work in specifically addressing species mapping.
Cite as

Jamie Scott, Kristin Stock, Fraser Morgan, Brandon Whitehead, and David Medyckyj-Scott. Automated Georeferencing of Antarctic Species. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part II. Leibniz International Proceedings in Informatics (LIPIcs), Volume 208, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{scott_et_al:LIPIcs.GIScience.2021.II.13,
  author =	{Scott, Jamie and Stock, Kristin and Morgan, Fraser and Whitehead, Brandon and Medyckyj-Scott, David},
  title =	{{Automated Georeferencing of Antarctic Species}},
  booktitle =	{11th International Conference on Geographic Information Science (GIScience 2021) - Part II},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-208-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{208},
  editor =	{Janowicz, Krzysztof and Verstegen, Judith A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2021.II.13},
  URN =		{urn:nbn:de:0030-drops-147726},
  doi =		{10.4230/LIPIcs.GIScience.2021.II.13},
  annote =	{Keywords: Named Entity Recognition (NER), Taxonomic Name Extraction, Relation Extraction, Georeferencing}
}
Document
DOI: 10.4230/LIPIcs.DNA.27.4
Improved Lower and Upper Bounds on the Tile Complexity of Uniquely Self-Assembling a Thin Rectangle Non-Cooperatively in 3D

Authors: David Furcy, Scott M. Summers, and Logan Withers

Published in: LIPIcs, Volume 205, 27th International Conference on DNA Computing and Molecular Programming (DNA 27) (2021)

Abstract
We investigate a fundamental question regarding a benchmark class of shapes in one of the simplest, yet most widely utilized abstract models of algorithmic tile self-assembly. More specifically, we study the directed tile complexity of a k × N thin rectangle in Winfree’s ubiquitous abstract Tile Assembly Model, assuming that cooperative binding cannot be enforced (temperature-1 self-assembly) and that tiles are allowed to be placed at most one step into the third dimension (just-barely 3D). While the directed tile complexities of a square and a scaled-up version of any algorithmically specified shape at temperature 1 in just-barely 3D are both asymptotically the same as they are (respectively) at temperature 2 in 2D, the (nearly tight) bounds on the directed tile complexity of a thin rectangle at temperature 2 in 2D are not currently known to hold at temperature 1 in just-barely 3D. Motivated by this discrepancy, we establish new lower and upper bounds on the directed tile complexity of a thin rectangle at temperature 1 in just-barely 3D. The proof of our upper bound is based on the construction of a novel, just-barely 3D temperature-1 self-assembling counter. Each value of the counter is comprised of k-2 digits, represented in a geometrically staggered fashion within k rows. This nearly optimal digit density, along with the base of the counter, which is proportional to N^{1/(k-1)}, results in an upper bound of O(N^{1/(k-1)} + log N), and is an asymptotic improvement over the previous state-of-the-art upper bound. On our way to proving our lower bound, we develop a new, more powerful type of specialized Window Movie Lemma that lets us bound the number of "sufficiently similar" ways to assign glues to a set (rather than a sequence) of fixed locations. Consequently, our lower bound, Ω(N^{1/k}), is also an asymptotic improvement over the previous state-of-the-art lower bound.
Cite as

David Furcy, Scott M. Summers, and Logan Withers. Improved Lower and Upper Bounds on the Tile Complexity of Uniquely Self-Assembling a Thin Rectangle Non-Cooperatively in 3D. In 27th International Conference on DNA Computing and Molecular Programming (DNA 27). Leibniz International Proceedings in Informatics (LIPIcs), Volume 205, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{furcy_et_al:LIPIcs.DNA.27.4,
  author =	{Furcy, David and Summers, Scott M. and Withers, Logan},
  title =	{{Improved Lower and Upper Bounds on the Tile Complexity of Uniquely Self-Assembling a Thin Rectangle Non-Cooperatively in 3D}},
  booktitle =	{27th International Conference on DNA Computing and Molecular Programming (DNA 27)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-205-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{205},
  editor =	{Lakin, Matthew R. and \v{S}ulc, Petr},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.27.4},
  URN =		{urn:nbn:de:0030-drops-146716},
  doi =		{10.4230/LIPIcs.DNA.27.4},
  annote =	{Keywords: Self-assembly, algorithmic self-assembly, tile self-assembly}
}
Document
DOI: 10.4230/LIPIcs.CCC.2019.9
Typically-Correct Derandomization for Small Time and Space

Authors: William M. Hoza

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)

Abstract
Suppose a language L can be decided by a bounded-error randomized algorithm that runs in space S and time n * poly(S). We give a randomized algorithm for L that still runs in space O(S) and time n * poly(S) that uses only O(S) random bits; our algorithm has a low failure probability on all but a negligible fraction of inputs of each length. As an immediate corollary, there is a deterministic algorithm for L that runs in space O(S) and succeeds on all but a negligible fraction of inputs of each length. We also give several other complexity-theoretic applications of our technique.
Cite as

William M. Hoza. Typically-Correct Derandomization for Small Time and Space. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 9:1-9:39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{hoza:LIPIcs.CCC.2019.9,
  author =	{Hoza, William M.},
  title =	{{Typically-Correct Derandomization for Small Time and Space}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{9:1--9:39},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.9},
  URN =		{urn:nbn:de:0030-drops-108317},
  doi =		{10.4230/LIPIcs.CCC.2019.9},
  annote =	{Keywords: Derandomization, pseudorandomness, space complexity}
}
Document
DOI: 10.4230/LIPIcs.TQC.2019.2
Quantum Distinguishing Complexity, Zero-Error Algorithms, and Statistical Zero Knowledge

Authors: Shalev Ben-David and Robin Kothari

Published in: LIPIcs, Volume 135, 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)

Abstract
We define a new query measure we call quantum distinguishing complexity, denoted QD(f) for a Boolean function f. Unlike a quantum query algorithm, which must output a state close to |0> on a 0-input and a state close to |1> on a 1-input, a "quantum distinguishing algorithm" can output any state, as long as the output states for any 0-input and 1-input are distinguishable. Using this measure, we establish a new relationship in query complexity: For all total functions f, Q_0(f)=O~(Q(f)^5), where Q_0(f) and Q(f) denote the zero-error and bounded-error quantum query complexity of f respectively, improving on the previously known sixth power relationship. We also define a query measure based on quantum statistical zero-knowledge proofs, QSZK(f), which is at most Q(f). We show that QD(f) in fact lower bounds QSZK(f) and not just Q(f). QD(f) also upper bounds the (positive-weights) adversary bound, which yields the following relationships for all f: Q(f) >= QSZK(f) >= QD(f) = Omega(Adv(f)). This sheds some light on why the adversary bound proves suboptimal bounds for problems like Collision and Set Equality, which have low QSZK complexity. Lastly, we show implications for lifting theorems in communication complexity. We show that a general lifting theorem for either zero-error quantum query complexity or for QSZK would imply a general lifting theorem for bounded-error quantum query complexity.
Cite as

Shalev Ben-David and Robin Kothari. Quantum Distinguishing Complexity, Zero-Error Algorithms, and Statistical Zero Knowledge. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bendavid_et_al:LIPIcs.TQC.2019.2,
  author =	{Ben-David, Shalev and Kothari, Robin},
  title =	{{Quantum Distinguishing Complexity, Zero-Error Algorithms, and Statistical Zero Knowledge}},
  booktitle =	{14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-112-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{135},
  editor =	{van Dam, Wim and Man\v{c}inska, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2019.2},
  URN =		{urn:nbn:de:0030-drops-103944},
  doi =		{10.4230/LIPIcs.TQC.2019.2},
  annote =	{Keywords: Quantum query complexity, quantum algorithms}
}
Document
DOI: 10.4230/LIPIcs.TQC.2019.8
A Compressed Classical Description of Quantum States

Authors: David Gosset and John Smolin

Published in: LIPIcs, Volume 135, 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)

Abstract
We show how to approximately represent a quantum state using the square root of the usual amount of classical memory. The classical representation of an n-qubit state psi consists of its inner products with O(sqrt{2^n}) stabilizer states. A quantum state initially specified by its 2^n entries in the computational basis can be compressed to this form in time O(2^n poly(n)), and, subsequently, the compressed description can be used to additively approximate the expectation value of an arbitrary observable. Our compression scheme directly gives a new protocol for the vector in subspace problem with randomized one-way communication complexity that matches (up to polylogarithmic factors) the optimal upper bound, due to Raz. We obtain an exponential improvement over Raz’s protocol in terms of computational efficiency.
Cite as

David Gosset and John Smolin. A Compressed Classical Description of Quantum States. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, pp. 8:1-8:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{gosset_et_al:LIPIcs.TQC.2019.8,
  author =	{Gosset, David and Smolin, John},
  title =	{{A Compressed Classical Description of Quantum States}},
  booktitle =	{14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)},
  pages =	{8:1--8:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-112-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{135},
  editor =	{van Dam, Wim and Man\v{c}inska, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2019.8},
  URN =		{urn:nbn:de:0030-drops-104005},
  doi =		{10.4230/LIPIcs.TQC.2019.8},
  annote =	{Keywords: Quantum computation, Quantum communication complexity, Classical simulation}
}
Document
DOI: 10.4230/LIPIcs.CCC.2016.26
Sculpting Quantum Speedups

Authors: Scott Aaronson and Shalev Ben-David

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

Abstract
Given a problem which is intractable for both quantum and classical algorithms, can we find a sub-problem for which quantum algorithms provide an exponential advantage? We refer to this problem as the "sculpting problem." In this work, we give a full characterization of sculptable functions in the query complexity setting. We show that a total function f can be restricted to a promise P such that Q(f|_P)=O(polylog(N)) and R(f|_P)=N^{Omega(1)}, if and only if f has a large number of inputs with large certificate complexity. The proof uses some interesting techniques: for one direction, we introduce new relationships between randomized and quantum query complexity in various settings, and for the other direction, we use a recent result from communication complexity due to Klartag and Regev. We also characterize sculpting for other query complexity measures, such as R(f) vs. R_0(f) and R_0(f) vs. D(f). Along the way, we prove some new relationships for quantum query complexity: for example, a nearly quadratic relationship between Q(f) and D(f) whenever the promise of f is small. This contrasts with the recent super-quadratic query complexity separations, showing that the maximum gap between classical and quantum query complexities is indeed quadratic in various settings - just not for total functions! Lastly, we investigate sculpting in the Turing machine model. We show that if there is any BPP-bi-immune language in BQP, then every language outside BPP can be restricted to a promise which places it in PromiseBQP but not in PromiseBPP. Under a weaker assumption, that some problem in BQP is hard on average for P/poly, we show that every paddable language outside BPP is sculptable in this way.
Cite as

Scott Aaronson and Shalev Ben-David. Sculpting Quantum Speedups. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 26:1-26:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{aaronson_et_al:LIPIcs.CCC.2016.26,
  author =	{Aaronson, Scott and Ben-David, Shalev},
  title =	{{Sculpting Quantum Speedups}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{26:1--26:28},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.26},
  URN =		{urn:nbn:de:0030-drops-58538},
  doi =		{10.4230/LIPIcs.CCC.2016.26},
  annote =	{Keywords: Quantum Computing, Query Complexity, Decision Tree Complexity, Structural Complexity}
}
Document
DOI: 10.4230/OASIcs.CMN.2014.130
A Flexible Framework for the Creation of Narrative-Centered Tools

Authors: James Niehaus, Victoria Romero, David Koelle, Noa Palmon, Bethany Bracken, Jonathan Pfautz, Scott Neal Reilly, and Peter Weyhrauch

Published in: OASIcs, Volume 41, 2014 Workshop on Computational Models of Narrative

Abstract
To better support the creation of narrative-centered tools, developers need a flexible framework to integrate, catalog, select, and reuse narrative models. Computational models of narrative enable the creation of software tools to aid narrative processing, analysis, and generation. Narrative-centered tools explicitly or implicitly embody one or more models of narrative by their definition. However, narrative model creation is often expensive and difficult with no guaranteed benefit to the end system. This paper describes our preliminary approach towards creating the SONNET narrative framework, a flexible framework to integrate, catalog, select, and reuse narrative models, thereby lowering development costs and improving benefits from each model. The framework includes a lightweight ontology language for the definition of key terms and interrelationships among them. The framework specifies model metadata to allow developers to discover and understand models more readily. We discuss the structure of this framework and ongoing development incorporating narrative models.
Cite as

James Niehaus, Victoria Romero, David Koelle, Noa Palmon, Bethany Bracken, Jonathan Pfautz, Scott Neal Reilly, and Peter Weyhrauch. A Flexible Framework for the Creation of Narrative-Centered Tools. In 2014 Workshop on Computational Models of Narrative. Open Access Series in Informatics (OASIcs), Volume 41, pp. 130-138, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{niehaus_et_al:OASIcs.CMN.2014.130,
  author =	{Niehaus, James and Romero, Victoria and Koelle, David and Palmon, Noa and Bracken, Bethany and Pfautz, Jonathan and Reilly, Scott Neal and Weyhrauch, Peter},
  title =	{{A Flexible Framework for the Creation of Narrative-Centered Tools}},
  booktitle =	{2014 Workshop on Computational Models of Narrative},
  pages =	{130--138},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-71-2},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{41},
  editor =	{Finlayson, Mark A. and Meister, Jan Christoph and Bruneau, Emile G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.CMN.2014.130},
  URN =		{urn:nbn:de:0030-drops-46511},
  doi =		{10.4230/OASIcs.CMN.2014.130},
  annote =	{Keywords: computational narrative, narrative analysis framework, narrative ontology, narrative models}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2461
Intrinsic Universality in Self-Assembly

Authors: David Doty, Jack H. Lutz, Matthew J. Patitz, Scott M. Summers, and Damien Woods

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates the assembly of any tile assembly system in a class of systems that we call \emph{locally consistent}: each tile binds with exactly the strength needed to stay attached, and that there are no glue mismatches between tiles in any produced assembly. Our construction is reminiscent of the studies of \emph{intrinsic universality} of cellular automata by Ollinger and others, in the sense that our simulation of a tile system $T$ by a tile system $U$ represents each tile in an assembly produced by $T$ by a $c \times c$ block of tiles in $U$, where $c$ is a constant depending on $T$ but not on the size of the assembly $T$ produces (which may in fact be infinite). Also, our construction improves on earlier simulations of tile assembly systems by other tile assembly systems (in particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we simulate the actual process of self-assembly, not just the end result, as in Soloveichik and Winfree's construction, and we do not discriminate against infinite structures. Both previous results simulate only temperature 1 systems, whereas our construction simulates tile assembly systems operating at temperature 2.
Cite as

David Doty, Jack H. Lutz, Matthew J. Patitz, Scott M. Summers, and Damien Woods. Intrinsic Universality in Self-Assembly. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 275-286, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{doty_et_al:LIPIcs.STACS.2010.2461,
  author =	{Doty, David and Lutz, Jack H. and Patitz, Matthew J. and Summers, Scott M. and Woods, Damien},
  title =	{{Intrinsic Universality in Self-Assembly}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{275--286},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2461},
  URN =		{urn:nbn:de:0030-drops-24619},
  doi =		{10.4230/LIPIcs.STACS.2010.2461},
  annote =	{Keywords: Biological computing, Molecular computation, intrinsic universality, self-assembly}
}
Document
DOI: 10.4230/DagSemProc.06271.11
MathBrush: An Experimental Pen-Based Math System

Authors: George Labahn, Scott MacLean, Marzouk Mirette, Ian Rutherford, and David Tausky

Published in: Dagstuhl Seminar Proceedings, Volume 6271, Challenges in Symbolic Computation Software (2006)

Abstract
It is widely believed that mathematics will be one of the major applications for Tablet PCs and other pen-based devices. In this paper we discuss many of the issues that make doing mathematics on such pen-based devices a hard task. We give a preliminary description of an experimental system, currently named MathBrush, for working with mathematics using pen-based devices. The system allows a user to enter mathematical expressions with a pen and to then do mathematical computation using a computer algebra system. The system provides a simple and easy way for users to verify the correctness of their handwritten expressions and, if needed, to correct any errors in recognition. Choosing mathematical operations is done making use of context menus, both with input and output expressions.
Cite as

George Labahn, Scott MacLean, Marzouk Mirette, Ian Rutherford, and David Tausky. MathBrush: An Experimental Pen-Based Math System. In Challenges in Symbolic Computation Software. Dagstuhl Seminar Proceedings, Volume 6271, pp. 1-8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{labahn_et_al:DagSemProc.06271.11,
  author =	{Labahn, George and MacLean, Scott and Marzouk Mirette and Rutherford, Ian and Tausky, David},
  title =	{{MathBrush: An Experimental Pen-Based Math System}},
  booktitle =	{Challenges in Symbolic Computation Software},
  pages =	{1--8},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6271},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06271.11},
  URN =		{urn:nbn:de:0030-drops-7733},
  doi =		{10.4230/DagSemProc.06271.11},
  annote =	{Keywords: PC Tablets, pen-based devices, computer algebra systems}
}
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