Examples of undecidable problems for 2-generator matrix semigroups

Theoretical Computer Science

Volumn 204, Issue 1-2, 1998, Pages 29-34

  Cassaigne, Julien ^a   Karhumäki, Juhani ^b  

^a AIX MARSEILLE UNIVERSITÉ   (France)

^b UNIVERSITY OF TURKU   (Finland)

Author keywords

Matrix problems; Two generator semigroup; Undecidability

Indexed keywords

EID: 0002841286     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(98)00029-2     Document Type: Article

References (10)

1. J. Berstel, C. Reutenauer, Rational Series and Their Languages, Springer, Berlin, 1988.
2. V. Blondel, J.N. Tsitsiklis, When is a Pair of Integer matrices Mortal?, Inform. Proc. Lett. 63 (1997) 283-286.
3. T. Harju, J. Karhumäki, Morphisms, in: G. Rozenberg, A. Salomaa, (Eds.), Handbook of Formal Languages, Springer, Berlin, 1997, pp. 439-510.
4. G. Jacob, La finitude des représentations linéaires de semi-groupes est décidable, J. Algebra 52 (1978) 437-459.
5. D.A. Klarner, J.-C. Birget, W. Satterfield, On the undecidability of the freeness of integer matrix semigroups, Int. J. Algebra Comput. 1 (1991) 223-226.
6. A. Mandel, I. Simon, On finite semigroups of matrices, Theoret. Comput. Sci. 5 (1997) 101-111.
7. Z. Manna, Mathematical Theory of Computations, McGraw-Hill, New York, 1974.
8. Y. Matiyasevich, G. Sénizergues, Decision problems for semi Thue systems with a few rules, in: Proc. LICS'96, IEEE Computer Society Press, Silver Spring, MD, 1996, pp. 523-531.
9. M.S. Paterson, Unsolvability in 3 x 3 matrices, Studies in Appl. Math. 49 (1970) 105-107.
10. A. Salomaa, M. Soittola, Automata-Theoretic Aspects of Formal Power Series, Springer, Berlin, 1978.