Skip to main content
SpringerLink
Log in

Leaf Language Classes

A Survey

  • Conference paper
Machines, Computations, and Universality (MCU 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3354))

Included in the following conference series:

Abstract

The theory of leaf language classes is a fruitful field of research which has been developed since the beginning of the nineties. The leaf language model, in which one language (or a pair of languages) defines a class of languages, allows a uniform definition and treatment of many complexity classes. The results of this area give new insights into the structure of complexity classes and their relation to other fields of Theoretical Computer Science.

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. Aaronson, S.: The complexity zoo, http://www.complexityzoo.com/

  2. Bovet, D.P., Crescenzi, P., Silvestri, R.: Complexity classes and sparse oracles. In: Proc. 6th IEEE Structure in Complexity Theory Conference, pp. 102–108 (1991); Journal of Computer and System Sciences 50, 382–390 (1995)

    Google Scholar 

  3. Bovet, D.P., Crescenzi, P., Silvestri, R.: A uniform approach to define complexity classes. Theoret. Comp. Sci 104, 263–283 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Balcázar, J.L., Díaz, J., Gabarró, J.: Structural Complexity I. EATCS Monographs on Theoretical Computer Science, vol. 11. Springer, Heidelberg (1988)

    MATH  Google Scholar 

  5. Balcáazar, J.L., Díaz, J., Gabarró, J.: Structural Complexity II. EATCS Monographs on Theoretical Computer Science, vol. 11. Springer, Heidelberg (1990)

    Google Scholar 

  6. Borchert, B.: On the Acceptance Power of Regular Languages. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 533–542. Springer, Heidelberg (1994); Final version: Theoretical Computer Science 148, 207–225 (1995)

    Google Scholar 

  7. Borchert, B.: Predicate Classes, Promise Classes, and the Acceptance Power of Regular Languages. Ph.D. thesis, Universität Heidelberg (1994)

    Google Scholar 

  8. Borchert, B.: Personal communication

    Google Scholar 

  9. Borchert, B., Kuske, D., Stephan, F.: On existentially first-order definable languages and their relation to NP. Theor. Informatics Appl. 33, 259–269 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Borchert, B., Lange, K.-J., Stephan, F., Tesson, P., Thérien, D.: The dot-depth and the polynomial hierarchy correspond on the delta levels. Technical Report 2004-2003, Wilhelm-Schickard-Institut, Universität Tübingen. To appear in the proceedingsof DLT 2004 (2004)

    Google Scholar 

  11. Borchert, B., Lozano, A.: Succinct Circuit Representations and Leaf Language Classes are Basically the Same Concept. Information Processing Letters 58, 211–215 (1996)

    Article  MathSciNet  Google Scholar 

  12. Borchert, B., Silvestri, R.: A Characterization of the Leaf Language Classes. Information Processing Letters 63, 153–158 (1997); Preliminary version: Borchert, B.: Predicate classes and promise classes. In: Proc. 9th Structure in Complexity Theory Conference, pp. 235–241 (1994)

    Google Scholar 

  13. Borchert, B., Silvestri, R.: Dot Operators. Theoretical Computer Science 262(1), 501–523 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. Burtschick, H.-J., Vollmer, H.: Lindström Quatifiers and Leaf Language Definability. Int. J. of Foundations of Computer Science 9, 277–294 (1998)

    Article  Google Scholar 

  15. Borchert, B., Schmitz, H., Stephan, F.: Unpublished manuscript (1999)

    Google Scholar 

  16. Cronauer, K., Hertrampf, U., Vollmer, H., Wagner, K.W.: The chain method to separate counting classes. Theory Comput. Systems 31, 93–108 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  17. Caussinus, H., McKenzie, P., Thérien, D., Vollmer, H.: Nondeterministic NC1 Computation. Journal of Computer and System Sciences 57, 200–212 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  18. Galota, M.: Blattsprachen und endliche Automaten. Technical Report No. 205, University of Würzburg, Department of Computer Science, 1

    Google Scholar 

  19. Galota, M., Kosub, S., Vollmer, H.: Generic Separations and Leaf Languages. To appear in Mathematical Logic Quarterly (2003)

    Google Scholar 

  20. Glaßer, C.: Counting with Counterfree Automata Electronic Colloquium on Computational Complexity, Report TR04-011, 2004. Technical Report No. 315, University of Würzburg (2004)

    Google Scholar 

  21. Goldschlager, L.M., Parberry, I.: On the Construction of Parallel Computers from Various Bases of Boolean Functions. Theoretical Computer Science 43, 43–58 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  22. Galota, M., Vollmer, H.: A generalization of the Büchi-Elgot-Trakhtenbrot theorem. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 355–368. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  23. Galota, M., Vollmer, H.: Functions computable in polynomial space (2003) (Manuscript)

    Google Scholar 

  24. Hertrampf, U.: Locally Definable Acceptance Types for Polynomial Time Machines. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 199–207. Springer, Heidelberg (1992)

    Google Scholar 

  25. Hertrampf, U.: Locally Definable Acceptance Types - the Three Valued Case. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 262–271. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  26. Hertrampf, U.: Complexity Classes with Finite Acceptance Types. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 543–553. Springer, Heidelberg (1994)

    Google Scholar 

  27. Hertrampf, U.: Complexity Classes Defined via k-Valued Functions. In: Proc. 9th Structure in Complexity Theory Conference, pp. 224–234 (1994)

    Google Scholar 

  28. Hertrampf, U., Lautemann, C., Schwentick, T., Vollmer, H., Wagner, K.W.: On the power of polynomial time bit-reductions. In: Proc. 8th Structure in Complexity Theory, pp. 200–207 (1993)

    Google Scholar 

  29. Hertrampf, U., Vollmer, H., Wagner, K.W.: On balanced vs. unbalanced computation trees. Math. Systems Theory 29, 411–421 (1996)

    MATH  MathSciNet  Google Scholar 

  30. Jenner, B., McKenzie, P., Thérien, D.: Logspace and logtime leaf languages. In: 9th Annual Conference on Structure in Complexity Theory, pp. 242–254 (1994); Information and Computation, 129, 21–33 (1996)

    Google Scholar 

  31. Kosub, S.: On NP-partitions over posets with an application to reducing the set of solutions of NP problems. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 467–476. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  32. Kosub, S., Schmitz, H., Vollmer, H.: Uniformly defining complexity classes of functions. International Journal of Foundations of Computer Science 11(4), 525–551 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  33. Niedermeier, R., Rossmanith, P.: Unambiguous computations and locally definable acceptance types. Theoretical Computer Science 194, 137–161 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  34. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)

    MATH  Google Scholar 

  35. Peichl, T., Vollmer, H.: Finite automata with generalized acceptance criteria. Discrete Mathematics and Theoretical Computer Science 4, 179–192 (2001)

    MATH  MathSciNet  Google Scholar 

  36. Pin, J.-E.: Syntactic semigroups. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of formal languages, vol. 1, pp. 679–746. Springer, Heidelberg (1996)

    Google Scholar 

  37. Schmitz, H.: The forbidden pattern approach to concatenation hierachies. Ph.D. Thesis, University of Würzburg 2000 (2000)

    Google Scholar 

  38. Schmitz, H., Wagner, K.: The Boolean Hierarchy over Level 1/2 of the Straubing-Therien Hierarchy. Technical Report No. 201, University of Würzburg, Department of Computer Science (1998)

    Google Scholar 

  39. Selivanov, V.L.: Relating automata-theoretic hierarchies to complexity-theoretic hierarchies. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 323–334. Springer, Heidelberg (2001); Final version: Theoret. Informatics Appl. 36, 29-42 (2002)

    Google Scholar 

  40. Selivanov, V.L., Wagner, K.W.: A reducibility for the dot-depth hierarchy. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 783–793. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  41. Travers, S.: Blattsprachen Komplexitätsklassen: Über Turing-Abschluss und Counting-Operatoren Studienarbeit, December 2002. Universität Würzburg (2002)

    Google Scholar 

  42. Vereshchagin, N.K.: Relativizable and non-relativizable theorems in the polynomial theory of algorithms. Izvestiya Rossiiskoi Akademii Nauk 57, 51–90 (1993) (in Russian)

    Google Scholar 

  43. Veith, H.: Succinct Representation, Leaf Languages and Projection Reductions. Information and Computation 142, 207–236 (1998); Preliminary version: Succinct Representation and Leaf Languages. In: Proc. 11th Annual IEEE Conference on Computational Complexity (CCC), pp. 118–126 (1996)

    Google Scholar 

  44. Vollmer, H.: Relating polynomial time to constant depth. Theoretial Computer Science 207, 159–170 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  45. Vollmer, H.: Uniform characterizations of complexity classes. ACM SIGACTNewsletter 30(1), 17–27 (1999)

    Article  Google Scholar 

  46. Vollmer, H.: Complexity theory made easy - the formal language approach to the definition of complexity classes. In: Proc. 7th Developments in Language Theory (2003)

    Google Scholar 

  47. Vollmer, H.: The Leaf Language Homepage, http://www.thi.uni-hannover.de/forschung/leafl/

  48. Wagner, K.W.: A reducibility and complete sets for the dot-depth hierarchy. Manuscript

    Google Scholar 

  49. Wagner, K.W.: New BCSV theorems. Technical Report 337, Institut für Informatik, Universität Würzburg

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Julius-Maximilians-Universität Würzburg,  

    Klaus W. Wagner

Authors
  1. Klaus W. Wagner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IUT de Metz, LITA, Université Paul Verlaine - Metz, EA 3097, UFR MIM, Île du Saulcy, 57045, Metz, Cédex, France

    Maurice Margenstern

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wagner, K.W. (2005). Leaf Language Classes. In: Margenstern, M. (eds) Machines, Computations, and Universality. MCU 2004. Lecture Notes in Computer Science, vol 3354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31834-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-31834-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25261-0

  • Online ISBN: 978-3-540-31834-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation