Advertisement

Rational transductions and complexity of counting problems

  • Christian Choffrut
  • Massimiliano Goldwurm
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)

Abstract

This work presents an algebraic method based on rational transductions to study the sequential and parallel complexity of counting problems for regular and context-free languages. This approach allows to obtain old and new results on the complexity of ranking and unranking as well as on other problems concerning the number of prefixes, suffixes, subwords and factors of a word which belong to a fixed language. Other results concern a suboptimal compression of finitely ambiguous c.f. languages, the complexity of the value problem for rational and algebraic formal series in noncommuting variables and a characterization of regular and Z-algebraic languages by means of rank functions.

Keywords

Formal Series Regular Language Regulate Representation Counting Problem Constant Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A.V. Aho, J.E. Hopcroft and J.D. Ullman, The design and analysis of computer algorithms, Addison-Wesley, Reading Mass. 1974.zbMATHGoogle Scholar
  2. [2]
    C. Alvarez and B. Jenner, “A very hard log space counting class”, Proceedings 5th Conference on Structure in Complexity Theory (1990), 154–168.Google Scholar
  3. [3]
    J. Berstel, Transductions and context-free languages, Teubner, Stuttgart, 1979.zbMATHGoogle Scholar
  4. [4]
    A. Bertoni, D. Bruschi and M. Goldwurm, “Ranking and formal power series”, Theoretical Computer Science 79 (1991) 25–35.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    A. Bertoni, M. Goldwurm and N. Sabadini, “The complexity of computing the number of strings of given length in context-free languages”, Theoretical Computer Science 86 (1991), 325–342.zbMATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    M. Bogni, Algoritmi per il problema del valore di serie formali a variabili non commutative, Degree Thesis in Mathematics, Dip. Scienze dell'Informazione, Università di Milano, June 1991.Google Scholar
  7. [7]
    S.A. Cook, “A taxonomy of problems with fast parallel algorithms,” Inform. and Control 64 (1985), 2–22.zbMATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    J. Earley, “An efficient context-free parsing algorithm”, Communications of the ACM 13 n.2 (1970),94–102.zbMATHCrossRefGoogle Scholar
  9. [9]
    P. Flajolet, “Analytic models and ambiguity of context-free languages”, Theoretical Computer Science 49 (1987), 283–309.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    A.V. Goldberg and M. Sipser, “Compression and ranking”, Proceedings 17th ACM Symp. on Theory of Comput. (1985), 59–68.Google Scholar
  11. [11]
    M. Harrison, Introduction to formal language theory, Addison-Wesley, Reading Mass., 1978.zbMATHGoogle Scholar
  12. [12]
    D.T. Huynh, “The complexity of ranking simple languages”, Math. Systems Theory 23 (1990), 1–20.zbMATHMathSciNetCrossRefGoogle Scholar
  13. [13]
    D.T. Huynh, “Effective entropies and data compression”, Information and Computation 90 (1991),67–85.zbMATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    A. Salomaa and M. Soittola, Automata theoretic aspects of formal power series, Springer Verlag, Berlin 1978.zbMATHGoogle Scholar
  15. [15]
    D.F. Stanat, “A homomorphism theorem for weighted context-free grammar”, J. Comput. System Sci. 6 (1972), 217–232.zbMATHMathSciNetGoogle Scholar
  16. [16]
    L.G. Valiant, “The complexity of enumeration and reliability problems”, SIAM J. Comput. 8 (1979), 410–420.zbMATHMathSciNetCrossRefGoogle Scholar
  17. [17]
    V. Vinaj, “Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits”, Proc. 6th Conference on Structure in Complexity Theory (1991), 270–284.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Christian Choffrut
    • 1
  • Massimiliano Goldwurm
    • 2
  1. 1.Laboratoire d'Informatique Théorique et ProgrammationUniversité Paris VIIFrance
  2. 2.Dip. Scienze dell'InformazioneUniversità di MilanoItaly

Personalised recommendations