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Diskretnaya Matematika, 2015, Volume 27, Issue 2, Pages 3–21
DOI: https://doi.org/10.4213/dm1322 (Mi dm1322) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Cardinality estimates for some classes of regular languages

D. E. Alexandrov

Lomonosov Moscow State University
Full-text PDF (541 kB) Citations (2)
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DOI: https://doi.org/10.4213/dm1322
Abstract: We consider a method that modifies regular expressions in order to solve the “exponential explosion” problem on the number of states of the finite automaton that recognizes a set of regular languages defined by the union of regular expressions of the form $.{*}$R$_1.{*}$R$_2.{*}$, where R$_1$ and R$_2$ are arbitrary regular expressions. We estimate the growth functions of regular languages from a subclass of the described class of regular languages and propose a method for estimation of relative growth of the number of words for the modification of a language defined by a pair of regular expressions. We also analyse practical efficiency of the proposed modification method and estimation method for the case of regular expressions from the system Snort.
Keywords: finite automata, regular expressions, intrusion detection systems.
Received: 25.02.2015
English version:
Discrete Mathematics and Applications, 2015, Volume 25, Issue 6, Pages 323–337
DOI: https://doi.org/10.1515/dma-2015-0031
Bibliographic databases:
Document Type: Article
UDC: 519.713.3
Language: Russian
Citation: D. E. Alexandrov, “Cardinality estimates for some classes of regular languages”, Diskr. Mat., 27:2 (2015), 3–21; Discrete Math. Appl., 25:6 (2015), 323–337
Citation in format AMSBIB
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\paper Cardinality estimates for some classes of regular languages
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\jour Discrete Math. Appl.
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  • https://www.mathnet.ru/eng/dm/v27/i2/p3
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретная математика
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    References:41
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