J. Cassaigne and J. Karhumaki. Examples of undecidable problems for 2-generator matrix semigroups. Theoretical Computer Science, 204(1), (1998) 29-34 Home/Search Document Details and Download
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On the Mortality Problem for Matrices of Low Dimensions - Bournez, Branicky (Correct)
....for rational matrices to the entry equivalence problem, to the zero in the corner problem, and to the reachability problem for piecewise ane functions. Finally, we state some NP completeness results. 1 Introduction Several undecidability results are known about problems involving matrices [6, 14]. For example, given a nite set F of matrices with integer entries, it is undecidable whether the semi group generated by M contains a matrix having a zero in the right upper corner [17] is free [11, 8] or contains the zero matrix [20] These problems have been proved to be undecidable when ....
....a zero in the right upper corner [17] is free [11, 8] or contains the zero matrix [20] These problems have been proved to be undecidable when restricted to 3 3 matrices. But for both of them, the question of their decidability or undecidability when restricted to 2 2 matrices remains open [6]. In this paper, we focus on the decidability of the latter problem. A set F = fA 1 ; Am g of d d matrices is said to be mortal if there exist an integer k 1 and some integers i 1 ; i 2 ; i k 2 f1; mg with A i 1 A i 2 A i k = 0. Therefore, we focus on the following ....
[Article contains additional citation context not shown here]
J. Cassaigne and J. Karhumaki. Examples of undecidable problems for 2generator matrix semigroups. Theoretical Computer Science, 204(1):29-34, September 1998.
Decision Questions on Integer Matrices - Harju (Correct)
....upper corner problem remains undecidable. This result is obtained by encoding several matrices into the diagonal of one matrix. This encoding was rst described by Turakainen [33] and then the undecidability was shown by Claus [8] for two matrices in Z 29 29 , see also Cassaigne and Karhum aki [5]. The present state of the Post Correspondence Problem, see [25] gives the following result by [8] Theorem 3.9. It is undecidable for subsemigroups S of N 23 23 generated by two matrices whether or not S has a matrix M with a zero in the upper right corner. 3.2 Mortality of matrices ....
....0 if and only if for each i, there exists a matrix M i 2 D with (M i ) ii = 0. In this case M ii = 0, where M = M 1 M 2 : M n , and M n = 0. The mortality problem is undecidable already for semigroups generated by two matrices. The order was bounded by 45 by Cassaigne and Karhum aki [5] and Blondel and Tsitsiklis [4] It was noticed by Halava and Harju [12] that the proof can be modi ed to give the bound 24 for the order of the matrices. 9 3.3 The problem of freeness Using the matrix representation we will obtain a result of Klarner, Birget and Satter eld [18] according ....
J. Cassaigne and J. Karhumaki, Examples of undecidable problems for 2-generator matrix semigroups, Theoret. Comput. Sci. 204 (1998), 29 { 34.
Mortality in Matrix Semigroups - Halava, Harju (2001) (Correct)
....(N a , a 2 , and BN 0 b1 ) Problem 1. Is the mortality problem undecidable for semigroups of 3 3 integer matrices with n generators for n 7 It is known that the mortality problem is undecidable for the semigroups generated by two matrices of dimension 45, see Casaigne and Karhumki [2] and Blondel and Tsitsiklis [1] The proof presented in [2] yields the dimension 24 using Theorem 5. Theorem 6. The mortality problem is undecidable for the semigroups generated by two integer matrices of dimension 24. Still, 24 is an impressive dimension for matrices. Problem 2. Is there a ....
.... problem undecidable for semigroups of 3 3 integer matrices with n generators for n 7 It is known that the mortality problem is undecidable for the semigroups generated by two matrices of dimension 45, see Casaigne and Karhumki [2] and Blondel and Tsitsiklis [1] The proof presented in [2] yields the dimension 24 using Theorem 5. Theorem 6. The mortality problem is undecidable for the semigroups generated by two integer matrices of dimension 24. Still, 24 is an impressive dimension for matrices. Problem 2. Is there a lower dimension d 24 for which the mortality problem is ....
J. Cassaigne and J. Karhumki, Examples of undecidable problems for 2generator matrix semigroups, In the special issue of Theoret. Comput. Sci. dedicated to M. P. Schtzenberger 204 (1998), 29--34.
On the Mortality Problem for Matrices of Low Dimensions - Bournez, Branicky (1999) (Correct)
....matrices to the entry equivalence problem, to the zero in the left upper corner problem and to the reachability problem for piecewise a ne functions. Finally, we state some NP completeness results. 1 Introduction Several undecidability results are known about problems involving matrices [5, 13]. For example, given a nite set F of matrices with integer entries, it is undecidable whether the semi group generated by M contains a matrix having a zero in the right upper corner [16] is free [10, 7] or contains the zero matrix [19] These problems have been proved to be undecidable when ....
....a zero in the right upper corner [16] is free [10, 7] or contains the zero matrix [19] These problems have been proved to be undecidable when restricted to 3 3 matrices. But for both of them the question of their decidability or undecidability when restricted to 2 2 matrices remains open [5]. In this paper, we focus on the decidability of the last problem. A set F = fA 1 ; Am g of d d matrices is said to be mortal if there exist an integer k 1 and some integers i 1 ; i 2 ; i k 2 f1; mg with A i 1 A i 2 A i k = 0. Hence, we focus on the following ....
[Article contains additional citation context not shown here]
J. Cassaigne and J. Karhumki. Examples of undecidable problems for 2generator matrix semigroups. Theoretical Computer Science, 204(1):2934, September 1998.
Decidable and Undecidable Problems in Matrix Theory - Halava (1997) (1 citation) (Correct)
....using the same method than the original proof of Paterson. We shall also consider the special case where the semigroup is generated by two matrices. It turns out that also in this case the mortality problem is undecidable if the dimension of the matrices is at least 45. This result is from [CKa]. In the third chapter we shall show that the method of Paterson does not suit for problems of 2 Theta 2 matrices. This result is from [CHK] It follows that for many problems, when we consider such matrices, it is not known whether they are decidable or not. In the fourth chapter we study the ....
....this problem is undecidable for matrices with dimension at least 3. The proof we present is from [Man] We shall also consider the case where semigroup is generated by two matrices and we prove that this problem is undecidable, when the dimension of the matrices is at least 24. This result is from [CKa]. In the seventh and eighth chapters we study the existence of a zero in the right upper corner in a matrix semigroup generated by one matrix. This problem is so called Skolem s problem. In the seventh chapter we will show that Skolem s problem is decidable for 2 Theta 2 matrices. The proof we ....
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J. Cassaigne and J. Karhumaki, Examples of undecidable problems for 2-generator matrix semigroups, TUCS Technical Report No 57.
Membership and Reachability Problems for Row-monomial.. - Lisitsa, Potapov (2004) (Correct)
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J. Cassaigne and J. Karhumaki. Examples of undecidable problems for 2-generator matrix semigroups. Theoretical Computer Science, 204(1), (1998) 29-34
The Mortality Problem for Matrices of Low Dimensions - Bournez, Branicky (2002) (Correct)
No context found.
J. Cassaigne and J. Karhumaki. Examples of undecidable problems for 2-generator matrix semigroups. Theoretical Computer Science, 204(1):29--34, September 1998.
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