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.
KeywordsNormal Form Finite System Empty Word Congruence Class Finite Alphabet
Unable to display preview. Download preview PDF.
- 1.A.V. Anisimov, Finite-automata semigroup mappings, Cybernetics, 5 (1981) 1–7.Google Scholar
- 2.J. Berstel, Congruences plus que parfaites et langages algébrique, Séminaire d'Informatique Théorique, Institut de Programmation (1976–77) 123–147.Google Scholar
- 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.J. Berstel and D. Perrin, Theory of Codes, Academic Press, 1985.Google Scholar
- 6.R. V. Book, Thue systems as rewriting systems, J. Symb. Comp. 3 (1987) 39–68.Google Scholar
- 7.R. V. Book and F. Otto, String-Rewriting Systems, Springer: New-York, 1993.Google Scholar
- 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.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.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