Skip to main content

Towards Decidability of Conjugacy of Pairs and Triples

  • Conference paper
Logic and Its Applications (ICLA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5378))

Included in the following conference series:

Abstract

The equation XZ = ZY is called the conjugacy equation. Here X, Y and Z are languages over a finite alphabet. Given two sets X and Y, we can ask “Does there exist a Z which makes the conjugacy equation true?”. We answer this question partially in the case when one of them is a two element set and the other is a three element set.

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. Chaitin, G.J.: Meta Math!: The Quest for Omega. Vintage Books (2006)

    Google Scholar 

  2. Lepistö, A.: Repetitions in Kolakoski sequence. In: Rozenberg, G., Salomaa, A. (eds.) Developments in Language Theory, pp. 130–143. WS (1994)

    Google Scholar 

  3. Kolakoski, W.G.: Elementary problem 5304. AMM 72, 674 (1965); Solution 73, 681–682 (1966)

    MathSciNet  Google Scholar 

  4. Berstel, J.: Axel Thue’s Papers on Repetitions in Words: a Translation. Publications du Laboratoire de Combinatoire et d’Informatique Mathématique. Université du Québec à Montréal (February 1995)

    Google Scholar 

  5. Thue, A.: Über unendliche Zeichenreihen. Norske vid. Selsk. Skr. Mat. Nat. Kl 7, 1–22 (1906); Thue, A., Nagell, T. (eds.) Selected Mathematical Papers, Universitetsforlaget, Oslo, pp. 139–158 (reprinted, 1977)

    Google Scholar 

  6. Makanin, G.S.: The problem of solvability of equations in a free semi-group. Math. USSR Sbornik 32(2), 129–198 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  7. Abdulrab, H.: Implementation of makanin’s algorithm. In: Schulz, K.U. (ed.) IWWERT 1990. LNCS, vol. 572, pp. 61–84. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  8. Koscielski, A., Pacholski, L.: Complexity of makanin’s algorithm. J. ACM 43(4), 670–684 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  9. Plandowski, W.: Satisfiability of word equations with constants is in pspace. J. ACM 51(3), 483–496 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cassaigne, J., Karhumäki, J., Manuch, J.: On conjugacy of languages. ITA 35(6), 535–550 (2001)

    MathSciNet  MATH  Google Scholar 

  11. Cassaigne, J., Karhumäki, J., Salmela, P.: Conjugacy of finite biprefix codes. In: Kunc, M., Okhotin, A. (eds.) Theory and Applications of Language Equations, Proceedings of the 1st International Workshop, July 2007, vol. 44, pp. 33–42. TUCS General Publication, Turku Centre for Computer Science (2007)

    Google Scholar 

  12. Knuth, D.E., Morris Jr., J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM J. Comput. 6(2), 323–350 (1977)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kenkireth, B.G., Ram, S. (2008). Towards Decidability of Conjugacy of Pairs and Triples. In: Ramanujam, R., Sarukkai, S. (eds) Logic and Its Applications. ICLA 2009. Lecture Notes in Computer Science(), vol 5378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92701-3_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-92701-3_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92700-6

  • Online ISBN: 978-3-540-92701-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics