License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.56
URN: urn:nbn:de:0030-drops-112717
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11271/
Go to the corresponding LIPIcs Volume Portal

Golovnev, Alexander ; Göös, Mika ; Reichman, Daniel ; Shinkar, Igor

String Matching: Communication, Circuits, and Learning

pdf-format:
LIPIcs-APPROX-RANDOM-2019-56.pdf (0.6 MB)

Abstract

String matching is the problem of deciding whether a given n-bit string contains a given k-bit pattern. We study the complexity of this problem in three settings.
- Communication complexity. For small k, we provide near-optimal upper and lower bounds on the communication complexity of string matching. For large k, our bounds leave open an exponential gap; we exhibit some evidence for the existence of a better protocol.
- Circuit complexity. We present several upper and lower bounds on the size of circuits with threshold and DeMorgan gates solving the string matching problem. Similarly to the above, our bounds are near-optimal for small k.
- Learning. We consider the problem of learning a hidden pattern of length at most k relative to the classifier that assigns 1 to every string that contains the pattern. We prove optimal bounds on the VC dimension and sample complexity of this problem.

BibTeX - Entry

@InProceedings{golovnev_et_al:LIPIcs:2019:11271,
  author =	{Alexander Golovnev and Mika G{\"o}{\"o}s and Daniel Reichman and Igor Shinkar},
  title =	{{String Matching: Communication, Circuits, and Learning}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{56:1--56:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Dimitris Achlioptas and L{\'a}szl{\'o} A. V{\'e}gh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11271},
  URN =		{urn:nbn:de:0030-drops-112717},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.56},
  annote =	{Keywords: string matching, communication complexity, circuit complexity, PAC learning}
}

Keywords: string matching, communication complexity, circuit complexity, PAC learning
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)
Issue Date: 2019
Date of publication: 17.09.2019

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI