Church-Rosser codes

  • Vladimir A. Oleshchuk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1025)


The notion of code, called Church-Rosser code, is proposed and studied. The necessary and sufficient conditions for a finite set of being a Church-Rosser code are presented. It is proved that property of being a Church-Rosser code defined by a monadic confluent stringrewriting system is decidable. We also propose decidable sufficient conditions for a finite set of being a Church-Rosser code defined by a finite Church-Rosser string-rewriting system.


Normal Form Finite System Empty Word Congruence Class Finite Alphabet 
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  1. 1.
    A.V. Anisimov, Finite-automata semigroup mappings, Cybernetics, 5 (1981) 1–7.Google Scholar
  2. 2.
    J. Berstel, Congruences plus que parfaites et langages algébrique, Séminaire d'Informatique Théorique, Institut de Programmation (1976–77) 123–147.Google Scholar
  3. 3.
    J. Berstel and L. Boasson, Context-free languages, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Vol. B, Elsevier Science Publishers B.V., 1990, 59–102.Google Scholar
  4. 4.
    J. Berstel and D. Perrin, Theory of Codes, Academic Press, 1985.Google Scholar
  5. 5.
    R. V. Book, Confluent and other types of Thue systems, Journal of ACM, 29 (1982) 171–183.CrossRefGoogle Scholar
  6. 6.
    R. V. Book, Thue systems as rewriting systems, J. Symb. Comp. 3 (1987) 39–68.Google Scholar
  7. 7.
    R. V. Book and F. Otto, String-Rewriting Systems, Springer: New-York, 1993.Google Scholar
  8. 8.
    D. Kapur, M. Krishnamoorthy, R. McNaughton and R. Narendran, An O(¦T¦ 3) algorithm for testing the Church-Rosser property of Thue systems, Theor. Comp. Sci. 35 (1985) 109–114.CrossRefGoogle Scholar
  9. 9.
    P. Narendran, C. O'Dunlaing and H. Rolletschek, Complexity of certain decision problems about congruential languages, J. Comp. Syst. Sci. 30, 343–358.Google Scholar
  10. 10.
    V. A. Oleshchuk, On public-key cryptosystem based on Church-Rosser stringrewriting systems, Computing and Combinatorics: First Annual International Conference (COCOON'95). Proceedings. LNCS 959 (1995) 264–269.Google Scholar
  11. 11.
    A. Sardinas and G. Patterson, A necessary and sufficient condition for the unique decomposition of coded messages, I.R.E. Int. Conv. Rec. 8 (1953) 104–108.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Vladimir A. Oleshchuk
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceAgder CollegeGrimstadNorway

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