Preview
Unable to display preview. Download preview PDF.
References
S. Adjan, Defining relations and algorithmic problems for groups and semigroups, Proc. Steklov Inst. Math. 85, 1966. (English version published by the American Mathematical Society, 1967.)
J. Avenhaus, R. Book, and C. Squier, On expressing commutativity by Church-Rosser presentations: a note on commutative monoids, R.A.I.R.O. Informatique Théorique 18 (1984), 47–52.
J. Avenhaus and K. Madlener, Algorithmische probleme bei einrelatorgruppen und ihre komplexität, Arch. Math. Logic 19 (1978), 3–12.
J. Avenhaus, K. Madlener, and F. Otto, Groups presented by finite two-monadic Church-Rosser Thue systems, Interner Bericht, Fachbereich Informatik, Univ. Kaiserslautern, 1984.
G. Bauer, Zur Darstellung von Monoiden durch Regelsysteme, Dissertation, Univ. Kaiserslautern, 1984.
G. Bauer, N-level rewriting systems, submitted for publication.
G. Bauer and F. Otto, Finite complete rewriting systems and the complexity of the word problem, Acta Informatica 21 (1984) 521–540.
J. Berstel, Congruences plus que parfaites et langages algébriques, Séminaire d'Informatique Théorique, Institut de Programmation, 1976–77, 123–147.
R. Book, Confluent and other types of Thue systems, J. Assoc. Computing Mach. 29 (1982), 171–183.
R. Book, When is a monoid a group? The Church-Rosser case is tractable, Theoret. Comput. Sci. 18 (1982), 325–331.
R. Book, A note on special Thue systems with a single defining relation, Math. Systems Theory 16 (1983), 301–312.
R. Book, Decidable questions of Church-Rosser congruences, Theoret. Comput. Sci. 24 (1983), 301–312.
R. Book, Homogeneous Thue systems and the Church-Rosser property, Discrete Math. 48 (1984), 137–145.
R. Book, M. Jantzen, and C. Wrathall, Monadic Thue systems, Theoret. Comput. Sci. 19 (1982), 231–251.
R. Book and C. O'Dúnlaing, Thue congruences and the Church-Rosser property, Semigroup Forum 22 (1981), 325–331.
R. Book and C. O'Dúnlaing, Testing for the Church-Rosser property, Theoret. Comput. Sci. 16(1981), 223–229.
R. Book and F. Otto, Cancellation rules and extended word problems, Information Proc. Letters 20 (1985), 5–11.
R. Book and F. Otto, On the security of two-party name-stamp protocols, Theoret. Comput. Sci., to appear.
R. Book and F. Otto, On the verifiability of two-party algebraic protocols, Theoret. Comput. Sci., to appear.
R. Book and C. Squier, Almost all one-rule Thue systems have decidable word problems, Discrete Math. 49 (1984), 237–240.
Y. Cochet, Sur l'algébricité des classes de certaines congruences définés sur le monoide libre. Thèse 3eme cycles, Rennes, 1971.
Y. Cochet, Church-Rosser congruences on free semigroups, Collog. Math. Soc. Janos Bolyai: Algebraic Theory of Semigroups 20 (1976), 51–60.
Y. Cochet and M. Nevat, Une généralization des ensembles de Dyck, Israel J. Math. 9 (1971), 389–395.
D. Dolev and A. Yao, On the security of public-key protocols, IEEE Trans. Information Theory IT-22 (1976), 644–654.
R. Gilman, Computations with rational subsets of confluent groups, in J. Fitch (ed.), EUROSAM 1984, Lecture Notes in Computer Science 174 (1984), 207–212.
G. Huet, Confluent reductions: abstract properties and applications to term-rewriting systems, J. Assoc. Comput. Mach. 27 (1980), 797–821.
G. Huet and D. Oppen, Equations and rewrite rules, in R. Book (ed.), Formal Language Theory: Perspectives and Open Problems, Academic Press, 1980, 349–405.
M. Jantzen, On a special monoid with a single defining relation, Theoret. Comput. Sci. 16 (1981), 61–73.
D. Kapur, M. Krishnamoorthy, R. McNaughton, and P. Narendran, An O(|T|3) algorithm for testing the Church-Rosser property of Thue systems, Theoret. Comput. Sci., 35 (1985), 109–114.
D. Kapur and P. Narendran, A finite Thue system with decidable word problem and without equivalent finite canonical system, Theoret. Comput. Sci., 35 (1985), 337–344.
D. Kapur and P. Narendran, The Knuth-Bendix completion procedure and Thue systems, SIAM J. Computing, to appear.
D. Knuth and P. Bendix, Simple word problems in universal algebras, in J. Leech (ed.), Computational Problems in Abstract Algebra, Pergamon Press, 1970, 263–297.
K. Madlener and F. Otto, Pseudo-natural algorithms for decision problems in certain types of string-rewriting systems, submitted for publication.
W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory, Wiley-Interscience, 1966.
Y. Metivier, Calcul de longuerurs de chaines de reecriture dans le monoide libre, Theoret. Comput. Sci. 35 (1985), 71–88.
D. Muller and P. Schupp, Groups, the theory of ends, and context-free languages, J. Comput. System Sci. 26 (1983), 295–310.
P. Narendran, Church-Rosser and Related Thue systems, Ph.D. Dissertation, Rennesselaer Poly. Institute, 1983. Also appears as Report No. 84CRD176, General Electric Corporate Research and Development Center, Schenectady, NY, 1984.
M. Nivat (avec M. Benois), Congruences parfaites, Seminaire Dubriels, 25e Année, 1971–72, 7-01-09.
C. O'Dúnlaing, Finite and Infinite Regular Thue Systems, Ph.D. Dissertation, Univ. of California at Santa Barbara, 1981.
C. O'Dúnlaing, Infinite regular Thue systems, Theoret. Comput. Sci., 25 (1983), 339–345.
C. O'Dúnlaing, Undecidable questions of Thue systems, Theoret. Comput. Sci., 23 (1983), 339–345.
F. Otto, Some undecidability results for non-monadic Church-Rosser Thue systems, Theoret. Comput. Sci., 33 (1984), 261–278.
F. Otto, Finite complete rewriting systems for the Jantzen monoid and the Greendlinger group, Theoret. Comput. Sci., 32 (1984), 249–260.
F. Otto, Church-Rosser Thue systems that present free monoids, SIAM J. Computing, to appear.
F. Otto, Elements of finite order for finite monadic Church-Rosser Thue systems, Trans. American Math. Soc., to appear.
F. Otto, Deciding algebraic properties of monoids presented by finite Church-Rosser Thue systems, Proc. First International Conference on Rewriting Techniques and Applications, Dijon, France, May 1985, Lecture Notes in Computer Science, to appear.
F. Otto, Decision Problems and their Complexity for Monadic Church-Rosser Thue Systems, in preparation.
F. Otto, and C. Wrathall, A note on Thue systems with a single defining relation, Math. Systems Theory, to appear.
L. Pan, On reduced Thue systems, Math. Systems Theory, to appear.
L. Pan, On the security of p-party protocols, submitted for publication.
D. Perrin and P. Schupp, Sure les monoids à un relateur qui sont des groupes, Theoret. Comput. Sci., 33 (1984), 331–334.
D. Potts, Remarks on an example of Jantzen, Theoret. Comput. Sci., 29 (1984), 277–284.
C. Squier, personal communication.
C. Squier and C. Wrathall, A note on representations of a certain monoid, Theoret. Comput. Sci., 17 (1982), 229–231.
A. Thue, Probleme über Veranderungen von Zeichenreihen nach gegeben Regeln, Skr. Vid. Kristianaia, I. Mat. Naturv. Klasse, No. 10 (1914), 34 pp.
C. Wrathall, On monoids and groups, in preparation.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Book, R.V. (1985). Thue systems as rewriting systems. In: Jouannaud, JP. (eds) Rewriting Techniques and Applications. RTA 1985. Lecture Notes in Computer Science, vol 202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15976-2_3
Download citation
DOI: https://doi.org/10.1007/3-540-15976-2_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15976-6
Online ISBN: 978-3-540-39679-6
eBook Packages: Springer Book Archive