Biprefix codes and semisimple algebras

  • Christophe Reutenauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 140)


We show here that there exists a close connection between the languagetheoretic concept of biprefixity and the classical algebraic concept of semisimplicity. More precisely, the main result is that, under suitable hypothesis, a (variablelength) code is biprefix if and only if its syntactic algebra is semisimple.


Formal Power Series Nilpotent Ideal Finite Codimension Semisimple Algebra Regular Code 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Berstel, D. Perrin, M.P. Schützenberger: the theory of codes, to appear.Google Scholar
  2. [2]
    A.H. Clifford, G.B. Preston: the algebraic theory of semigroups, A.M.S.(61).Google Scholar
  3. [3]
    S. Eilenberg: automata, languages and machines, vol. A, Acad. Press (1974)Google Scholar
  4. [4]
    I.N. Herstein: noncommutative rings, Carus mathematical monograph (1969).Google Scholar
  5. [5]
    G. Lallement: semigroups and combinatorial applications, John Wiley (1979)Google Scholar
  6. [6]
    C. Reutenauer: séries formelles et algèbres syntactiques, J. Algebra 66, 448–483 (1980).MathSciNetCrossRefGoogle Scholar
  7. [7]
    A. Salomaa, M. Soittola: automata-theoretic aspects of formal power series, Springer Verlag (1977).Google Scholar
  8. [8]
    M.P. Schützenberger: on the definition of a family of automata, Information and Control 4, 245–270 (1961).MathSciNetCrossRefGoogle Scholar
  9. [9]
    M.P. Schützenberger: on a special class of recurrent events, Annals of Math. Stat. 32, 1201–1213 (1961).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Christophe Reutenauer
    • 1
  1. 1.LITP Institut de ProgrammationParisFrance

Personalised recommendations