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Property testing of regular languages with applications to streaming property testing of visibly pushdown languages

Abstract : In this work, we revisit the problem of testing membership in regular languages, first studied by Alon et al. [1]. We develop a one-sided error property tester for regular languages under weighted edit distance that makes O((1/ε) 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 O((1/ε)^4 log^6 n) to O((1/ε)^3 log^5 n log log n), where n is the size of the input. Finally, we provide aΩ(max((1/ε) , 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.
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https://hal.archives-ouvertes.fr/hal-03219254
Contributor : Tatiana Starikovskaya Connect in order to contact the contributor
Submitted on : Friday, May 7, 2021 - 10:40:07 AM
Last modification on : Friday, October 15, 2021 - 1:39:55 PM
Long-term archiving on: : Sunday, August 8, 2021 - 6:13:15 PM

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Gabriel Bathie, Tatiana Starikovskaya. Property testing of regular languages with applications to streaming property testing of visibly pushdown languages. ICALP 2021, 2021, GLASGOW (virtual conference), United Kingdom. ⟨10.4230/LIPIcs.ICALP.2021.115⟩. ⟨hal-03219254⟩

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