The complexity of the characteristic and the minimal polynomial

Theoretical Computer Science

Volumn 295, Issue 1-3, 2003, Pages 205-222

  Hoang, Thanh Minh ^a   Thierauf, Thomas ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

Characteristic polynomial; Computational complexity; Invariant factors; Linear algebra; Logspace counting classes; Minimal polynomial

Indexed keywords

COMPUTATIONAL METHODS; MATRIX ALGEBRA; POLYNOMIALS; PROBLEM SOLVING;

MINIMAL POLYNOMIALS;

COMPUTATIONAL COMPLEXITY;

EID: 0037463545     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(02)00404-8     Document Type: Conference Paper

References (26)

1. E. Allender, V. Arvind, M. Mahajan, Arithmetic complexity, Kleene closure, and formal power series, 1999, Available at http://www.cs.rutgers.edu/̃allender/publications.
2. Allender E., Beals R., Ogihara M. The complexity of matrix rank and feasible systems of linear equations. Comput. Complexity. 8:1999;99-126.
3. Berkowitz S. On computing the determinant in small parallel time using a small number of processors. Inform. Process. Lett. 18:1984;147-150.
4. Brualdi R., Ryser H. Combinatorial Matrix Theory. Encyclopedia of Mathematics and its Applications. Vol. 39:1991;Cambridge University Press, Cambridge.
5. Cook S. A taxonomy of problems with fast parallel algorithms. Inform. Control. 64:1985;2-22.
6. Cvetković D., Doob M., Sachs H. Spectra of Graphs, Theory and Application. 1980;Academic Press, New York.
7. (#L) (1985), Technical Report Informatik-Preprint 8, Fachbereich Informatik der Humboldt-Universität zu Berlin, 1991.
8. Fenner S., Fortnow L., Kurtz S. Gap-definable counting classes. J. Comput. System Sci. 48:1994;116-148.
9. F. Gantmacher, The Theory of Matrices, Vols. 1 and 2, AMS Chelsea Publishing, Providence, RI, 1977.
10. Horn R., Johnson C. Matrix Analysis. 1985;Cambridge University Press, Cambridge.
11. Immerman N. Nondeterministic space is closed under complement. SIAM J. Comput. 17:1988;935-938.
12. Kaltofen E., Saunders B. Fast parallel computation of Hermite and Smith forms of polynomial matrices. SIAM Algebraic Discrete Methods. 8:1987;683-690.
13. M. Mahajan, V. Vinay, Determinant: combinatorics, algorithms, and complexity, Chicago J. Theoret. Comput. Sci. (5) (1997).
14. Mahajan M., Vinay V. Determinant. old algorithms, new insights SIAM J. Discrete Math. 12(4):1999;474-490.
15. N. Nisan, A. Ta-Shma, Symmetric logspace is closed under complement, Chicago J. Theoret. Comput. Sci. (1) (1995).
16. K. Reinhardt, E. Allender, Making nondeterminism unambiguous, in: 38th Symp. on Foundation of Computer Science, IEEE Computer Society Press, Silver Spring, MD, 1997, pp. 244-253.
17. Santha M., Tan S. Verifying the determinant in parallel. Comput. Complexity. 7:1998;128-151.
18. 3) algorithm for Frobenius normal form, in: Internat. Symp. on Symbolic and Algebraic Computation (ISSAC), 1998.
19. Szelepcsényi R. The method of forced enumeration for nondeterministic automata. Acta Inform. 26(3):1988;279-284.
20. S. Toda, Counting problems computationally equivalent to the determinant, Technical Report CSIM 91-07, Department of Computer Science and Information Mathematics, University of Electro-Communications, Chofu-shi, Tokyo, Japan, 1991.
21. Valiant L. The complexity of computing the permanent. Theoret. Comput. Sci. 8:1979;189-201.
22. Valiant L. The complexity of enumeration and reliability problems. SIAM J. Comput. 8:1979;410-421.
23. Valiant L. Why is boolean complexity theory difficult. Paterson M.S. Boolean Function Complexity. London Mathematical Society Lecture Notes Series. Vol. 169:1992;Cambridge University Press, Cambridge.
24. Villard G. Fast parallel algorithms for matrix reduction to normal forms. Appl. Algebra Eng. Comm. Comput. (AAECC). 8:1997;511-537.
25. V. Vinay, Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits, in: 6th IEEE Conf. on Structure in Complexity Theory, 1991, pp. 270-284.
26. Zeilberger D. A combinatorial approach to matrix algebra. Discrete Math. 56:1985;61-72.