Skip to main content

Rational Selecting Relations and Selectors

  • Conference paper
  • First Online:
Language and Automata Theory and Applications (LATA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8977))

  • 1400 Accesses

Abstract

We consider rational relations made of pairs \((u,v)\) of finite words such that \(v\) is a subword of \(u\). We show that such a selecting relation can be realized by a transducer such that the output label of each transition is a subword of its input label. We also show that it is decidable whether a given relation has this property.

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

Access this chapter

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agafonov, V.N.: Normal sequences and finite automata. Soviet Mathematics Doklady 9, 324–325 (1968)

    MATH  Google Scholar 

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

    Google Scholar 

  3. Carton, O.: The growth ratio of synchronous rational relations is unique. Theoret. Comput. Sci. 376, 52–59 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Choffrut, C., Karhumäki, J.: On Fatou properties of rational languages. In: Where Mathematics, Computer Science, Linguistics and Biology Meet: Essays in Honour of Gheorghe Paun. Kluwer Academic Publishers (2001)

    Google Scholar 

  5. Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press, New York (1972)

    Google Scholar 

  6. Elgot, C.C., Mezei, J.E.: On relations defined by generalized finite automata. IBM Journal Res. and Dev. 9, 47–68 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  7. Higman, G.: Ordering by divisibility in abstract algebra. Proc. London Math. Soc. 2, 326–336 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  8. Leguy, J.: Transductions rationnelles décroissantes. R.A.I.R.O.-Informatique Théorique et Applications 5, 141–148 (1981)

    MathSciNet  Google Scholar 

  9. Lothaire, M.: Combinatorics on Words, Encyclopedia of Mathematics and its Applications, vol. 17. Addison-Wesley, Reading (1983)

    Google Scholar 

  10. Perrin, D., Pin, J.É.: Infinite Words. Elsevier (2004)

    Google Scholar 

  11. Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Olivier Carton .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Boasson, L., Carton, O. (2015). Rational Selecting Relations and Selectors. In: Dediu, AH., Formenti, E., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science(), vol 8977. Springer, Cham. https://doi.org/10.1007/978-3-319-15579-1_56

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-15579-1_56

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15578-4

  • Online ISBN: 978-3-319-15579-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics