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Link to original content: https://doi.org/10.4230/LIPIcs.ITCS.2020.79
Pseudo-Deterministic Streaming
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Pseudo-Deterministic Streaming

Authors Shafi Goldwasser, Ofer Grossman, Sidhanth Mohanty, David P. Woodruff

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Author Details

Shafi Goldwasser
  • Simons Institute for the Theory of Computing, Berkeley, CA, USA
  • MIT, Cambridge, MA, USA
Ofer Grossman
  • MIT, Cambridge, MA, USA
Sidhanth Mohanty
  • University of California Berkeley, CA, USA
David P. Woodruff
  • Carnegie-Mellon University, Pittsburgh, PA, USA

Funding

  • Goldwasser, Shafi: Supported by NSF CNS-1413920, DARPA/NJIT 491512803, Sloan Foundation 996698, and MIT/IBM W1771646. This work was done at the Simons Institute for the Theory of Computing.
  • Grossman, Ofer: Supported by the Fannie and John Hertz Foundation fellowship, an NSF GRFP award, NSF CNS-1413920, DARPA/NJIT 491512803, Sloan Foundation 996698, and MIT/IBM W1771646. This work was done in part at the Simons Institute for the Theory of Computing.
  • Mohanty, Sidhanth: Supported by NSF grant CCF-1718695. This work was done in part at the Simons Institute for the Theory of Computing.
  • Woodruff, David P.: Supported by the National Science Foundation under Grant No. CCF-1815840. This work was done in part at the Simons Institute for the Theory of Computing.

Cite As Get BibTex

Shafi Goldwasser, Ofer Grossman, Sidhanth Mohanty, and David P. Woodruff. Pseudo-Deterministic Streaming. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 79:1-79:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ITCS.2020.79

Abstract

A pseudo-deterministic algorithm is a (randomized) algorithm which, when run multiple times on the same input, with high probability outputs the same result on all executions. Classic streaming algorithms, such as those for finding heavy hitters, approximate counting, ?_2 approximation, finding a nonzero entry in a vector (for turnstile algorithms) are not pseudo-deterministic. For example, in the instance of finding a nonzero entry in a vector, for any known low-space algorithm A, there exists a stream x so that running A twice on x (using different randomness) would with high probability result in two different entries as the output.
In this work, we study whether it is inherent that these algorithms output different values on different executions. That is, we ask whether these problems have low-memory pseudo-deterministic algorithms. For instance, we show that there is no low-memory pseudo-deterministic algorithm for finding a nonzero entry in a vector (given in a turnstile fashion), and also that there is no low-dimensional pseudo-deterministic sketching algorithm for ?_2 norm estimation. We also exhibit problems which do have low memory pseudo-deterministic algorithms but no low memory deterministic algorithm, such as outputting a nonzero row of a matrix, or outputting a basis for the row-span of a matrix.
We also investigate multi-pseudo-deterministic algorithms: algorithms which with high probability output one of a few options. We show the first lower bounds for such algorithms. This implies that there are streaming problems such that every low space algorithm for the problem must have inputs where there are many valid outputs, all with a significant probability of being outputted.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • streaming
  • pseudo-deterministic

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