K. Culik II and J. Karhumaki, Systems of equations over a free monoid and Ehrenfeucht 's conjecture. Discrete Mathematics 43 (1983) 139--153. Home/Search Document Not in Database Summary Related Articles Check |
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A Note on Decidability Questions on Presentations of.. - Choffrut, Harju.. (Correct)
....relation by Lemma 2.1, and thus it is sufficient to show that the problem whether a rational relation K is equivalent to R is decidable. This problem reduces, again by Lemma 2.1, to checking whether two finite 5 relations K 0 and R are equivalent. The latter problem was shown to be decidable in [5] by using Makanin s result, which states that one can effectively test whether an equation has a solution in a free semigroup. ut The analysis problem for finite F presententation is still open: Problem 1 For given finite X and R X is it decidable whether or not [X ; R] is an ....
K. Culik II and J. Karhumaki, Systems of equations over a free monoid and Ehrenfeucht's Conjecture, Discrete Math. 43 (1983), 139 -- 153.
On the Independence of Equations in Three Variables - Harju, Nowotka (2001) (Correct)
....own right, it also provides more insight into the following question: Does there exist an independent system of three equations in three variables that has a nonperiodic solution If it does, it must contain balanced equations only. This question was implicitely raised by Culik II and Karhum aki [3] rst in 1983. This introduction is followed by the preliminaries, Section 2, where the notations for this article are xed. Section 3 introduces Spehner s [7] characterization of solutions of equations in three variables which is compared with an earlier result by Budkina and Markov [1] in ....
K. Culik II and J. Karhumaki. Systems of equations over a free monoid and ehrenfeucht conjecture. Discrete Mathematics, 43:139-153, 1983.
Some Open Problems in Combinatorics of Words and Related Areas - Karhumäki (2000) Self-citation (Karhum) (Correct)
....y = b, and the system is independent as shown by the triples (x; y; z) a; b; aba) and (x; y; z) a; b; abba) Historical remarks. The original formulation of the Ehrenfeucht Compactness Property was in language theoretic set up, cf. KI] Its equivalence to the one stated here was noticed in [CuKII]. Problem 1 became natural when the validity of the Ehrenfeucht Compactness Property was established for free semigroups in 1985, cf. ALII] and [G] Surprisingly very little progress on the problem has been achieved, see however [KPlI] and [KPlII] It is also worth mentioning that although the ....
.... on the problem has been achieved, see however [KPlI] and [KPlII] It is also worth mentioning that although the compactness property holds both in free groups and in abelian monoids the answer to Problem 1 is negative in both of these cases, see [ALI] and [KPlI] Problem 3 occurred implicitely in [CuKII] and more explicitely in [KPlII] 3 4 Cumulative defect e ect Another fundamental property of words is revealed in so called defect theorem, which states that if a set X of n nonempty words satis es a nontrivial relation then there exists an F such that X F (1) and ....
Culik II, K. and Karhumaki, J., Systems of equations over a free monoid and Ehrenfeucht's conjecture, Discrete Math. 43, 1983, 139-153.
Patterns - Salomaa (2003) (Correct)
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K. Culik II and J. Karhumaki, Systems of equations over a free monoid and Ehrenfeucht 's conjecture. Discrete Mathematics 43 (1983) 139--153.
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