On quadratic word equations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1563, Issue , 1999, Pages 217-226

  Robson, John Michael ^a   Diekert, Volker ^b  

^a UNIVERSITÉ DE BORDEAUX   (France)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

CORRESPONDING SOLUTIONS; MINIMAL SOLUTIONS; NEW RESULTS; PSPACE-COMPLETE; QUADRATIC SYSTEMS; SATISFIABILITY PROBLEMS; SINGLE EQUATION; WORD EQUATIONS;

FORMAL LOGIC;

EID: 84983197001     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-49116-3_20     Document Type: Conference Paper

References (24)

1. Habib Abdulrab and Jean-Pierre Péecuchet. Solving word equations. J. Symbolic Computation, 8(5):499-521, 1990.
2. Habib Abdulrab and Jean-Pierre Péecuchet, editors. Proceedings of Word Equations and Related Topics (IWWERT '91), volume 677 of Lect. Notes Comp. Sci. Springer-Verlag, Berlin, Heidelberg, New York, 1993.
3. Thierry Arnoux. Untersuchungen zum Makaninschen Algorithmus. Diplomarbeit 1613, Universität Stuttgart, 1998.
4. Christian Choffrut and Juhani Karhumäki. Combinatorics of words. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, Vol. 1, pages 329-438. Springer-Verlag, Berlin, Heidelberg, New York, 1997.
5. Volker Diekert. Makanin's Algorithm. In Jean Berstel and Dominique Perrin, editors, Algebraic Combinatorics on Words. Cambridge University Press. A preliminary version is on the web: http://www-igm.univ-mlv.fr/ berstel/Lothaire/index.html.
6. Volker Diekert, Yuri Matiyasevich, and Anca Muscholl. Solving trace equations using lexicographical normal forms. In P. Degano, R. Gorrieri, and A. Marchetti-Spaccamela, editors, Proc. of the 24th ICALP, Bologna, 1997, number 1256 in Lect. Notes Comp. Sci., pages 336-347. Springer-Verlag, Berlin, Heidelberg, New York, 1997.
7. Claudio Gutiérrez. Satisfiability of word equations with constants is in exponential space. In Proc. of the 39th Ann. Symp. on Foundations of Computer Science, FOCS 98, pages 112-119, Los Alamitos, California, 1998. IEEE Computer Society Press.
8. John E. Hopcroft and Jeffrey D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, Mass., 1979.
9. Joxan Jaffar. Minimal and complete word unification. J. Assoc. Comput. Mach., 37(1):47-85, 1990.
10. Antoni Kośscielski and Leszek Pacholski. Complexity of Makanin's algorithm. J. Assoc. Comput. Mach., 43(4):670-684, 1996. Preliminary version in Proc. of the 31st Annual IEEE Symposium on Foundations of Computer Science, Los Alamitos, 1990.
11. th Ann. Symp. on Foundations of Computer Science, FOCS 77, pages 254-266. IEEE Computer Society Press, 1977.
12. Roger C. Lyndon. Equations in free groups. Transactions of the American Mathematical Society, 96, 1960.
13. Roger C. Lyndon and Paul E. Schupp. Combinatorial Group Theory. Springer-Verlag, Berlin, Heidelberg, New York, 1977.
14. Gennadií S. Makanin. The problem of solvability of equations in a free semigroup. Mat. Sb., 103(2):147-236, 1977. In Russian; English translation in: Math. USSR Sbornik, 32, 129-198, 1977.
15. Andrei A. Markov. Theory of Algorithms. Academy of Sciences of the USSR, 1954. English translation, Add. Wesley 1981.
16. Yuri Matiyasevich. A connection between systems of word and length equations and Hilbert's Tenth Problem. Sem. Mat. V. A. Steklov Math. Inst. Leningrad, 8:132-144, 1968. In Russian; English translation in: Seminars in Mathematics, V. A. Steklov Mathematical Institute, 8, 61-67, 1970.
17. Yuri Matiyasevich. Some decision problems for traces. In Sergej Adian and Anil Nerode, editors, Proceedings of the 4th International Symposium on Logical Foundations of Computer Science (LFCS'97), Yaroslavl, Russia, July 6-12, 1997, number 1234 in Lect. Notes Comp. Sci., pages 248-257. Springer-Verlag, Berlin, Heidelberg, New York, 1997.
18. Jakob Nielsen. Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden. Mathematische Annalen, 78, 1918.
19. Dominique Perrin. Equations in words. In H. Ait-Kaci and M. Nivat, editors, Resolution of equations in algebraic structures, Vol. 2, pages 275-298. Academic Press, 1989.
20. John Michael Robson. Word equations with at most 2 occurrences of each variable. Preprint, LaBRI, Université de Bordeaux I, 1998.
21. Wojciech Rytter and Wojciech Plandowski. Application of Lempel-Ziv encodings to the solution of words equations. In Kim G. Larsen et al., editors, Proc. of the 25th ICALP, Aarhus, 1998, number 1443 in Lect. Notes Comp. Sci., pages 731-742. Springer-Verlag, Berlin, Heidelberg, New York, 1998.
22. Klaus U. Schulz. Makanin's algorithm for word equations: Two improvements and a generalization. In K.-U. Schulz, editor, Proceedings of Word Equations and Related Topics, 1st International Workshop, IWWERT'90, Tübingen, Germany, volume 572 of Lect. Notes Comp. Sci., pages 85-150. Springer-Verlag, Berlin, Heidelberg, New York, 1992.
23. Klaus U. Schulz, editor. Proceedings of Word Equations and Related Topics (IWWERT '90), volume 572 of Lect. Notes Comp. Sci. Springer-Verlag, Berlin, Heidelberg, New York, 1992.
24. Klaus U. Schulz. Word unification and transformation of generalized equations. Journal of Automated Reasoning, 11(2):149-184, 1993.