Skip to main content
SpringerLink
Log in

An Equivalence Relation on the Class of Regular Languages

  • Conference paper
  • First Online:
Convergent Cognitive Information Technologies (Convergent 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1140))

  • 497 Accesses

Abstract

This paper introduces a special binary relation on the set of regular languages, which possesses all three properties of equivalence relation. That is, this relation separates the whole class of regular languages into non-intersecting classes. In addition, it allows us to consider only one representative of each class in the description of the regular languages class, the so-called “simplified” language. Such simplified language corresponds to a “simplified” automaton. This equivalence relation makes it possible to limit the number of considered regular languages to a finite number of finite automata with a priori fixed number of states. In addition, this equivalence relation preserves the relation \(\#\) considered in our previous papers, and therefore allows us to use the previous theory. For example, on the basis of obtained results, we can apply various algorithms of equivalent transformations of nondeterministic finite automata to simplified them.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    For example, \(\delta \) corresponds to \(\gamma \), \(\widetilde{\delta }\) corresponds to \(\widetilde{\gamma }\), etc.

  2. 2.

    Like [1], we name “canonical automaton” a deterministic automaton, containing the minimum possible number of states. Here, also like [1], we do not require this automaton to be the everywhere-defined, and, therefore, do not consider the possible “dead state”.

  3. 3.

    Let us note once again, that according to the previous agreement,

    $$ \widetilde{K} = \left( \widetilde{Q},\varSigma ,\widetilde{\delta },\widetilde{S},\widetilde{F}\right) . $$

    .

References

  1. Melnikov, B.: Once more on the edge-minimization of nondeterministic finite automata and the connected problems. Fundam. Informaticae 104(3), 267–283 (2010)

    Article  MathSciNet  Google Scholar 

  2. Melnikov, B., Tsyganov, A.: The state minimization problem for nondeterministic finite automata: the parallel implementation of the truncated branch and bound method. In: Proceedings of the International Symposium on Parallel Architectures, Algorithms and Programming, PAAP-2012, Taipei, Taiwan, pp. 194–201 (2012)

    Google Scholar 

  3. Melnikov, B., Dolgov, V.: Some more algorithms for Conway’s universal automaton. Acta Univ. Sapientiae, Informatica. 6(1), 5–20 (2014)

    Article  Google Scholar 

  4. Melnikov, B.: The complete finite automaton. Int. J. Open Inf. Technol. 5(10), 9–17 (2017)

    Google Scholar 

  5. Melnikov, B.: The star-height of a finite automaton and some related questions. Int. J. Open Inf. Technol. 6(7), 1–5 (2018)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shenzhen MSU-BIT University, No. 1, International University Park Road, Dayun New Town, Longgang District, Shenzhen, 518172, Guangdong Province, China

    Boris Melnikov

  2. Ulyanovsk State Polytechnical University – Terenga Liceum, No. 32, Severnyy Venec Street, Ulyanovsk, 432027, Russia

    Vasily Dolgov

  3. Russian State Social University, Wilhelm Pieck str., 4, Moscow, 129226, Russia

    Elena Melnikova

Authors
  1. Boris Melnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vasily Dolgov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elena Melnikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Boris Melnikov .

Editor information

Editors and Affiliations

  1. Moscow State University, Moscow, Russia

    Vladimir Sukhomlin

  2. Moscow State University, Moscow, Russia

    Elena Zubareva

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Melnikov, B., Dolgov, V., Melnikova, E. (2020). An Equivalence Relation on the Class of Regular Languages. In: Sukhomlin, V., Zubareva, E. (eds) Convergent Cognitive Information Technologies. Convergent 2018. Communications in Computer and Information Science, vol 1140. Springer, Cham. https://doi.org/10.1007/978-3-030-37436-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-37436-5_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-37435-8

  • Online ISBN: 978-3-030-37436-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation