3 Search Results for "Menuhin, Boaz"

Document

DOI: 10.4230/LIPIcs.CCC.2024.28

Finding Missing Items Requires Strong Forms of Randomness

Authors: Amit Chakrabarti and Manuel Stoeckl

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

Adversarially robust streaming algorithms are required to process a stream of elements and produce correct outputs, even when each stream element can be chosen as a function of earlier algorithm outputs. As with classic streaming algorithms, which must only be correct for the worst-case fixed stream, adversarially robust algorithms with access to randomness can use significantly less space than deterministic algorithms. We prove that for the Missing Item Finding problem in streaming, the space complexity also significantly depends on how adversarially robust algorithms are permitted to use randomness. (In contrast, the space complexity of classic streaming algorithms does not depend as strongly on the way randomness is used.) For Missing Item Finding on streams of length 𝓁 with elements in {1,…,n}, and ≤ 1/poly(𝓁) error, we show that when 𝓁 = O(2^√{log n}), "random seed" adversarially robust algorithms, which only use randomness at initialization, require 𝓁^Ω(1) bits of space, while "random tape" adversarially robust algorithms, which may make random decisions at any time, may use O(polylog(𝓁)) random bits. When 𝓁 is between n^Ω(1) and O(√n), "random tape" adversarially robust algorithms need 𝓁^Ω(1) space, while "random oracle" adversarially robust algorithms, which can read from a long random string for free, may use O(polylog(𝓁)) space. The space lower bound for the "random seed" case follows, by a reduction given in prior work, from a lower bound for pseudo-deterministic streaming algorithms given in this paper.

Cite as

Amit Chakrabarti and Manuel Stoeckl. Finding Missing Items Requires Strong Forms of Randomness. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chakrabarti_et_al:LIPIcs.CCC.2024.28,
  author =	{Chakrabarti, Amit and Stoeckl, Manuel},
  title =	{{Finding Missing Items Requires Strong Forms of Randomness}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.28},
  URN =		{urn:nbn:de:0030-drops-204242},
  doi =		{10.4230/LIPIcs.CCC.2024.28},
  annote =	{Keywords: Data streaming, lower bounds, space complexity, adversarial robustness, derandomization, sketching, sampling}
}

Document

DOI: 10.4230/LIPIcs.FUN.2022.20

Mirror Games Against an Open Book Player

Authors: Roey Magen and Moni Naor

Published in: LIPIcs, Volume 226, 11th International Conference on Fun with Algorithms (FUN 2022)

Abstract

Mirror games were invented by Garg and Schnieder (ITCS 2019). Alice and Bob take turns (with Alice playing first) in declaring numbers from the set {1,2, …, 2n}. If a player picks a number that was previously played, that player loses and the other player wins. If all numbers are declared without repetition, the result is a draw. Bob has a simple mirror strategy that assures he won't lose and requires no memory. On the other hand, Garg and Schenier showed that every deterministic Alice needs memory of size linear in n in order to secure a draw. Regarding probabilistic strategies, previous work showed that a model where Alice has access to a secret random perfect matching over {1,2, …, 2n} allows her to achieve a draw in the game w.p. a least 1-1/n and using only polylog bits of memory. We show that the requirement for secret bits is crucial: for an "open book" Alice with no secrets (Bob knows her memory but not future coin flips) and memory of at most n/4c bits for any c ≥ 2, there is a Bob that wins w.p. close to 1-{2^{-c/2}}.

Cite as

Roey Magen and Moni Naor. Mirror Games Against an Open Book Player. In 11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 20:1-20:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{magen_et_al:LIPIcs.FUN.2022.20,
  author =	{Magen, Roey and Naor, Moni},
  title =	{{Mirror Games Against an Open Book Player}},
  booktitle =	{11th International Conference on Fun with Algorithms (FUN 2022)},
  pages =	{20:1--20:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-232-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{226},
  editor =	{Fraigniaud, Pierre and Uno, Yushi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2022.20},
  URN =		{urn:nbn:de:0030-drops-159900},
  doi =		{10.4230/LIPIcs.FUN.2022.20},
  annote =	{Keywords: Mirror Games, Space Complexity, Eventown-Oddtown}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2022.107

Keep That Card in Mind: Card Guessing with Limited Memory

Authors: Boaz Menuhin and Moni Naor

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract

A card guessing game is played between two players, Guesser and Dealer. At the beginning of the game, the Dealer holds a deck of n cards (labeled 1, ..., n). For n turns, the Dealer draws a card from the deck, the Guesser guesses which card was drawn, and then the card is discarded from the deck. The Guesser receives a point for each correctly guessed card. With perfect memory, a Guesser can keep track of all cards that were played so far and pick at random a card that has not appeared so far, yielding in expectation ln n correct guesses, regardless of how the Dealer arranges the deck. With no memory, the best a Guesser can do will result in a single guess in expectation. We consider the case of a memory bounded Guesser that has m < n memory bits. We show that the performance of such a memory bounded Guesser depends much on the behavior of the Dealer. In more detail, we show that there is a gap between the static case, where the Dealer draws cards from a properly shuffled deck or a prearranged one, and the adaptive case, where the Dealer draws cards thoughtfully, in an adversarial manner. Specifically: 1) We show a Guesser with O(log² n) memory bits that scores a near optimal result against any static Dealer. 2) We show that no Guesser with m bits of memory can score better than O(√m) correct guesses against a random Dealer, thus, no Guesser can score better than min {√m, ln n}, i.e., the above Guesser is optimal. 3) We show an efficient adaptive Dealer against which no Guesser with m memory bits can make more than ln m + 2 ln log n + O(1) correct guesses in expectation. These results are (almost) tight, and we prove them using compression arguments that harness the guessing strategy for encoding.

Cite as

Boaz Menuhin and Moni Naor. Keep That Card in Mind: Card Guessing with Limited Memory. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 107:1-107:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{menuhin_et_al:LIPIcs.ITCS.2022.107,
  author =	{Menuhin, Boaz and Naor, Moni},
  title =	{{Keep That Card in Mind: Card Guessing with Limited Memory}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{107:1--107:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.107},
  URN =		{urn:nbn:de:0030-drops-157039},
  doi =		{10.4230/LIPIcs.ITCS.2022.107},
  annote =	{Keywords: Adaptivity vs Non-adaptivity, Adversarial Robustness, Card Guessing, Compression Argument, Information Theory, Streaming Algorithms, Two Player Game}
}

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2 Naor, Moni
1 Chakrabarti, Amit
1 Magen, Roey
1 Menuhin, Boaz
1 Stoeckl, Manuel

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1 Theory of computation → Adversary models
1 Theory of computation → Lower bounds and information complexity
1 Theory of computation → Pseudorandomness and derandomization
1 Theory of computation → Sketching and sampling
1 Theory of computation → Streaming models

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1 Adaptivity vs Non-adaptivity
1 Adversarial Robustness
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