Skip to main content
SpringerLink
Log in

Why We Need Semirings in Automata Theory (Extended Abstract)

  • Conference paper
  • First Online:
Algebraic Informatics (CAI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9270))

Included in the following conference series:

  • 581 Accesses

Abstract

In this lecture we will report on generalizations of some classical results on formal languages. These generalizations are achieved by an algebraic treatment using semirings, formal power series, fixed point theory and matrices. By the use of these mathematical constructs, definitions, constructions, and proofs are obtained that are very satisfactory from a mathematical point of view.

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 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

References

  1. Baron, G., Kuich, W.: The characterization of nonexpansive grammars by rational power series. Inf. Control 48, 109–118 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  2. Berstel, J.: Transductions and Context-Free Languages. Teubner (1979)

    Google Scholar 

  3. Ésik, Z., Kuich, W.: On power series over a graded monoid. In: Calude, C.S., Freivalds, R., Kazuo, I. (eds.) Gruska Festschrift. LNCS, vol. 8808, pp. 49–55. Springer, Heidelberg (2014)

    Google Scholar 

  4. Flajolet, P.: Ambiguity and transcendence. In: Brauer, W. (ed.) Automata, Languages and Programming. LNCS, pp. 179–188. Springer, Heidelberg (1985)

    Chapter  Google Scholar 

  5. Harju, T., Karhumäki, J.: The equivalence problem of multitape finite automata. Theoretical Computer Science 78, 347–355 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kuich, W.: On the entropy of context-free languages. Inf. Control 16, 173–200 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kuich, W.: Forty years of formal power series in automata theory. In: Salomaa, A., Wood, D., Yu, S. (eds.) Half Century of Automata Theory, pp. 49–71. World Scientific (2001)

    Google Scholar 

  8. Kuich, W., Salomaa, A.: Semirings, Automata, Languages. Springer (1986)

    Google Scholar 

  9. Sakarovitch, J.: Rational and recognisable power series. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, Chapter 4, pp. 105–174. Springer (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Wien, Vienna, Austria

    Werner Kuich

Authors
  1. Werner Kuich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Werner Kuich .

Editor information

Editors and Affiliations

  1. Institut für Maschinelle, Universität Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Andreas Maletti

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kuich, W. (2015). Why We Need Semirings in Automata Theory (Extended Abstract). In: Maletti, A. (eds) Algebraic Informatics. CAI 2015. Lecture Notes in Computer Science(), vol 9270. Springer, Cham. https://doi.org/10.1007/978-3-319-23021-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23021-4_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23020-7

  • Online ISBN: 978-3-319-23021-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation