Skip to main content
SpringerLink
Log in

Complexity Issues for Preorders on Finite Labeled Forests

  • Conference paper
Models of Computation in Context (CiE 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6735))

Included in the following conference series:

  • 491 Accesses

Abstract

We prove that three preorders on the finite k-labeled forests are polynomial time computable. Together with an earlier result of the first author, this implies polynomial-time computability for an important initial segment of the corresponding degrees of discontinuity of k-partitions on the Baire space. Furthermore, we show that on ω-labeled forests the first of these three preorders is polynomial time computable as well while the other two preorders are NP-complete.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Balcázar, J.L., Díaz, J., Gabarró, J.: Structural complexity. I. In: EATCS Monographs on Theoretical Computer Science, vol. 11, Springer, Berlin (1988)

    Google Scholar 

  2. Balcázar, J.L., Díaz, J., Gabarró, J.: Structural complexity II. In: EATCS Monographs on Theoretical Computer Science, vol. 22, Springer, Berlin (1990)

    Google Scholar 

  3. Brattka, V., Gherardi, G.: Effective choice and boundedness principles in computable analysis. Bulletin of Symbolic Logic 17(1), 73–117 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brattka, V., Gherardi, G.: Weihrauch degrees, omniscience principles and weak computability. J. Symb. Log. 76(1), 143–176 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Davey, B., Priestley, H.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  6. Downey, R.G., Fellows, M.R.: Parameterized Complexity Theory. Monographs in Computer Science. Springer, New York (1999)

    Book  MATH  Google Scholar 

  7. Hertling, P.: A topological complexity hierarchy of functions with finite range. Technical Report 223, Centre de recerca matematica, Institut d’estudis catalans, Barcelona, Workshop on Continuous Algorithms and Complexity (October 1993)

    Google Scholar 

  8. Hertling, P.: Topologische Komplexitätsgrade von Funktionen mit endlichem Bild. Informatik Berichte 152, FernUniversität Hagen, Hagen (December 1993)

    Google Scholar 

  9. Hertling, P.: Unstetigkeitsgrade von Funktionen in der effektiven Analysis. PhD thesis, Fachbereich Informatik, FernUniversität Hagen (1996)

    Google Scholar 

  10. Hirsch, M.D.: Applications of topology to lower bound estimates in computer science. In: Hirsch, M.W., et al. (eds.) From topology to computation: Proceedings of the Smalefest, pp. 395–418. Springer, New York (1993)

    Chapter  Google Scholar 

  11. Kechris, A.S.: Classical descriptive set theory.. Graduate Texts in Mathematics, vol. 156. Springer, Berlin (1995)

    MATH  Google Scholar 

  12. Kosub, S.: NP-partitions over posets with an application to reducing the set of solutions of NP problems. Theory Comput. Syst. 38(1), 83–113 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kosub, S., Wagner, K.W.: The Boolean Hierarchy of NP-Partitions. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 157–168. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Kudinov, O.V., Selivanov, V.L.: Undecidability in the Homomorphic Quasiorder of Finite Labeled Forests. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds.) CiE 2006. LNCS, vol. 3988, pp. 289–296. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Kudinov, O.V., Selivanov, V.L.: Undecidability in the homomorphic quasiorder of finite labelled forests. J. Log. Comput. 17(6), 1135–1151 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kudinov, O.V., Selivanov, V.L.: A Gandy Theorem for Abstract Structures and Applications to First-Order Definability. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds.) CiE 2009. LNCS, vol. 5635, pp. 290–299. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Kudinov, O.V., Selivanov, V.L., Zhukov, A.V.: Undecidability in Weihrauch Degrees. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds.) CiE 2010. LNCS, vol. 6158, pp. 256–265. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  18. Kwuida, L., Lehtonen, E.: On the homomorphism order of labeled posets. Order (2010)

    Google Scholar 

  19. Lehtonen, E.: Labeled posets are universal. Eur. J. Comb. 29(2), 493–506 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Selivanov, V.: Boolean hierarchies of partitions over a reducible base. Algebra Logika 43(1), 77–109 (2004); Translation in Algebra and Logic 43(1), 44-61

    Article  MathSciNet  MATH  Google Scholar 

  21. Selivanov, V.L.: Hierarchies of \(\Delta^0_2\)–measurable k–partitions. Mathematical Logic Quarterly 53(4–5), 446–461 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. von Stein, T.: Vergleich nicht konstruktiv lösbarer Probleme in der Analysis. Diplomarbeit, Fakultät für Informatik, FernUniversität Hagen (March 1989)

    Google Scholar 

  23. Weihrauch, K.: The degrees of discontinuity of some translators between representations of the real numbers. Informatik Berichte 129, FernUniversität Hagen, Hagen (July 1992)

    Google Scholar 

  24. Weihrauch, K.: The TTE-interpretation of three hierarchies of omniscience principles. Informatik Berichte 130, FernUniversität Hagen, Hagen (September 1992)

    Google Scholar 

  25. Weihrauch, K.: Computable Analysis. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Informatik, Mathematik und Operations Research, Universität der Bundeswehr München, 85577, Neubiberg, Germany

    Peter Hertling

  2. A.P. Ershov Institute of Informatics Systems, Lavrentyev av. 6, 630090, Novosibirsk, Russia

    Victor Selivanov

Authors
  1. Peter Hertling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Victor Selivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

  2. Department of Mathematics, University of Oslo, 0316, Oslo, Norway

    Dag Normann

  3. Department of Mathematical Logic and Applications, Sofia University, 1164, Sofia, Bulgaria

    Ivan Soskov  & Alexandra Soskova  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hertling, P., Selivanov, V. (2011). Complexity Issues for Preorders on Finite Labeled Forests. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21875-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21874-3

  • Online ISBN: 978-3-642-21875-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation