License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.119
URN: urn:nbn:de:0030-drops-141881
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14188/
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Bathie, Gabriel ; Starikovskaya, Tatiana

Property Testing of Regular Languages with Applications to Streaming Property Testing of Visibly Pushdown Languages

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LIPIcs-ICALP-2021-119.pdf (0.8 MB)

Abstract

In this work, we revisit the problem of testing membership in regular languages, first studied by Alon et al. [Alon et al., 2001]. We develop a one-sided error property tester for regular languages under weighted edit distance that makes ?(ε^{-1} log(1/ε)) non-adaptive queries, assuming that the language is described by an automaton of constant size. Moreover, we show a matching lower bound, essentially closing the problem for the edit distance. As an application, we improve the space bound of the current best streaming property testing algorithm for visibly pushdown languages from ?(ε^{-4} log⁶ n) to ?(ε^{-3} log⁵ n log log n), where n is the size of the input. Finally, we provide a Ω(max(ε^{-1}, log n)) lower bound on the memory necessary to test visibly pushdown languages in the streaming model, significantly narrowing the gap between the known bounds.

BibTeX - Entry

@InProceedings{bathie_et_al:LIPIcs.ICALP.2021.119,
  author =	{Bathie, Gabriel and Starikovskaya, Tatiana},
  title =	{{Property Testing of Regular Languages with Applications to Streaming Property Testing of Visibly Pushdown Languages}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{119:1--119:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14188},
  URN =		{urn:nbn:de:0030-drops-141881},
  doi =		{10.4230/LIPIcs.ICALP.2021.119},
  annote =	{Keywords: property testing, regular languages, streaming algorithms, visibly pushdown languages}
}

Keywords: property testing, regular languages, streaming algorithms, visibly pushdown languages
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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