Volker Diekert, Claudio Gutierrez, and Christian Hagenah. The existential theory of equations with rational constraints in free groups is PSPACE-complete. In A. Ferreira and H. Reichel, editors, Proc. of the 18th STACS (STACS'01), Dresden, Lecture Notes in Computer Science 2010. Home/Search Document Details and Download
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The Existential Theory of Equations with Rational.. - Diekert.. (2001) (1 citation) Self-citation (Diekert Guti Christian) (Correct)
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Volker Diekert, Claudio Gutierrez, and Christian Hagenah. The existential theory of equations with rational constraints in free groups is PSPACE-complete. In A. Ferreira and H. Reichel, editors, Proc. of the 18th STACS (STACS'01), Dresden, Lecture Notes in Computer Science 2010.
Solvability of Equations in Free Partially - Commutative Groups Is Self-citation (Diekert) (Correct)
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V. Diekert, C. Guti'errez, and C. Hagenah. The existential theory of equations with rational constraints in free groups is PSPACE-complete. In Proc. 18th Ann. Symp. on Theor. Aspects of Comp. Sci. (STACS'01), LNCS 2010:170--182, Springer, 2001.
Existential and Positive Theories of Equations in Graph Products - Diekert, Lohrey (2002) Self-citation (Diekert) (Correct)
....Since the seminal work of Makanin [19] on equations in free monoids, the decidability of various theories of equations in di erent monoids and groups has been studied, and several new decidability and complexity results have been shown. Let us mention here the results of [25, 27] for free monoids, [6, 15, 20, 21] for free groups, 9] for free partially commutative monoids (trace monoids) 10] for free partially commutative groups (graph groups) and [7] for plain groups (free products of nite and free groups) In this paper we continue this stream of research. We will present two main results. The rst ....
....has at most k complete thin clans and an existential formula with constraints in NRAT(GP) QUESTION: Does belong to Th(G P; NRAT(G P) If the number of complete thin clans of (V; E) is not bounded, then the problem above is in EXPSPACE. Remark 1. Formally, Theorem 1 generalizes results of [6, 7, 9, 10, 15, 19, 20, 25]. For this it is enough to give a reduction to the main result of [10] The next lemma is the main technical tool for proving the theorem above. First we need some further de nitions concerning traces. The set IC M IRR(S) consists of all traces a 1 an , a i 2 , such that (a i ; a j ) 2 ....
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V. Diekert, C. Gutierrez, and C. Hagenah. The existential theory of equations with rational constraints in free groups is PSPACE-complete. In Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science (STACS 01), number 2010 in Lecture Notes in Computer Science, pages 170-182. Springer, 2001.
The Existential Theory of Equations with Rational.. - Diekert.. (1 citation) Self-citation (Diekert Guti'errez Hagenah) (Correct)
....equations in free groups has been replaced by a polynomial space bounded algorithm. Hagenah and Diekert worked independently in the same direction and using some ideas of Guti errez they obtained a result which includes the presence of rational constraints. This appeared as extended abstract in [4] and also as a part of the PhD thesis of Hagenah [11] The present paper is a journal version of [4, 10] It shows that the existential theory of equations in free groups with rational constraints is PSPACE complete. Rational constraints mean that a possible solution has to respect a ....
....worked independently in the same direction and using some ideas of Guti errez they obtained a result which includes the presence of rational constraints. This appeared as extended abstract in [4] and also as a part of the PhD thesis of Hagenah [11] The present paper is a journal version of [4, 10]. It shows that the existential theory of equations in free groups with rational constraints is PSPACE complete. Rational constraints mean that a possible solution has to respect a specification which is given by a regular word language. The idea to consider regular constraints for word ....
Volker Diekert, Claudio Guti'errez, and Christian Hagenah. The existential theory of equations with rational constraints in free groups is PSPACE-complete. In A. Ferreira and H. Reichel, editors, Proc. of the 18th STACS (STACS'01), Dresden, Lecture Notes in Computer Science 2010.
Recognizing String Graphs in NP - Schaefer, Sedgwick, Stefankovic (2002) (Correct)
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Volker Diekert, Claudio Gutierrez, and Christian Hagenah. Existential theory of equations with rational constraints in free groups is PSPACE-complete. In Proceedings of the 18th International Symposium on Theoretical Aspects of Computer Science, STACS 2001, 2001.
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