Non-looping string rewriting
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) no. 3, pp. 279-301.
@article{ITA_1999__33_3_279_0,
     author = {Geser, Alfons and Zantema, Hans},
     title = {Non-looping string rewriting},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {279--301},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {3},
     year = {1999},
     zbl = {0951.68054},
     mrnumber = {1728428},
     language = {en},
     url = {http://www.numdam.org/item/ITA_1999__33_3_279_0/}
}
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Geser, Alfons; Zantema, Hans. Non-looping string rewriting. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) no. 3, pp. 279-301. http://www.numdam.org/item/ITA_1999__33_3_279_0/

[1] S. Adjan and G. Oganesjan, Problems of equality and divisibility in semigroups with a single defining relation. Mat. Zametki 41 (1987) 412-421. | Zbl 0617.20035

[2] R. Book and F. Otto, String-rewriting systems. Texts and Monographs in Computer Science. Springer, New York (1993). | MR 1215932 | Zbl 0832.68061

[3] N. Dershowitz, Termination of linear rewriting Systems. In Proc. of the 8th International Colloquium on Automata, Languages and Programming (ICALP81), Springer, Lecture Notes in Computer Science 115 (1981) 448-458. | MR 826061 | Zbl 0465.68009

[4] N. Dershowitz, Termination of rewriting. J. Symb. Comput. 3 (1987) 69-115; Corrigendum 4 (1987) 409-410. | MR 893186

[5] N. Dershowitz and C. Hoot, Natural termination. Theoret. Comput. Sci. 142 (1995) 179-207. | MR 1334808 | Zbl 0873.68103

[6] M. Ferreira and H. Zantema, Dummy elimination: Making termination easier. In Proc. l0th Conf. Fundamentals of Computation Theory, H. Reichel, Ed., Springer, Lecture Notes in Computer Science 965 (1995) 243-252. | MR 1459181

[7] A. Geser, Termination of one-rule string rewriting Systems l → r where |r| ≤ 9. Tech. Rep., Universität Tübingen, D (Jan. 1998).

[8] J. V. Guttag, D. Kapur and D. R. Musser, On proving uniform termination and restricted termination of rewriting systems. SIAM J. Comput. 12 (1983) 189-214. | MR 687810 | Zbl 0526.68036

[9] G. Huet and D. S. Lankford, On the uniform halting problem for term rewriting Systems. Rapport Laboria 283, INRIA (1978).

[10] M. Jantzen, Confluent string rewriting, Vol. 14 of EATCS Monographs on Theoretical Computer Science. Springer, Berlin (1988). | MR 972260 | Zbl 1097.68572

[11] Y. Kobayashi, M. Katsura and K. Shikishima-Tsuji, Termination and derivational complexity of confluent one-rule string rewriting Systems. Tech. Rep., Dept. of Computer Science, Toho University, JP (1997).

[12] W. Kurth, Termination und Konfluenz von Semi-Thue-Systemen mit nur einer Regel. Dissertation, Technische Universität Clausthal, Germany (1990). | Zbl 0719.03019

[13] W. Kurth, One-rule semi-Thue Systems with loops of length one, two, or three. RAIRO Theoret. Informatics Appl. 30 (1995) 415-429. | Numdam | Zbl 0867.68064

[14] D. S. Lankford and D. R. Musser, A finite termination criterion. Tech. Rep., Information Sciences Institute, Univ. of Southern California, Marina-del-Rey, CA (1978).

[15] Y. Matiyasevitch and G. Sénizergues, Decision problems for semi-Thue systems with a few rules. In IEEE Symp. Logic in Computer Sdence'96 (1996).

[16] R. Mcnaughton, The uniform halting problem for one-rule Semi-Thue Systems. Tech. Rep. 94-18, Dept. of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, Aug. 1994.

See also "Correction to The Uniform Halting Problem for One-rule Semi-Thue Systems", Personal communication (Aug. 1996).

[17] R. Mcnaughton, Well-behaved derivations in one-rule Semi-Thue Systems. Tech. Rep. 95-15, Dept. of Computer Science, Rensselaer Polytechnic Institute, Troy, NY (Nov. 1995).

[18] R. Mcnaughton, Semi-Thue Systems with an inhibitor. Tech. Rep. 97-5, Dept. of Computer Science, Rensselaer Polytechnic Institute, Troy, NY (1 1997).

[19] F. Otto, The undecidability of self-embedding for finite semi-Thue and Thue Systems. Theoret. Comput. Sci. 47 (1986) 225-232. | MR 881214 | Zbl 0624.03032

[20] B.K. Rosen, Tree-manipulating Systems and Church-Rosser Theorems.J. ACM 20 (1973). 160-187. | MR 331850 | Zbl 0267.68013

[21] K. Shikishima-Tsuji, M. Katsura and Y. Kobayashi, On termination of confluent one-rule string rewriting Systems. Inform. Process, Lett. 61 (1997), 91-96. | MR 1439874

[22] C. Wrathall, Confluence of one-rule Thue Systems. In Word Equations and Related Topics, K.U. Schulz, Ed., Springer, Lecture Notes in Computer Science 572 (1991). | MR 1232039

[23] H. Zantema and A. Geser, A complete characterization of termination of 0p1q → lr0s. Applicable Algebra in Engineering, Communication, and Computing. In print. | Zbl 0962.68086

[24] H. Zantema and A. Geser, A complete characterization of termination of 0p1q → lr0s. In Proc. of the 6th Conference on Rewriting Techniques and Applications, J. Hsiang, Ed., Springer, Lecture Notes in Computer Science 914 (1995) 41-55.