The complexity of matrix rank and feasible systems of linear equations

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn Part F129452, Issue , 1996, Pages 161-167

  Allender, Eric ^a   Beals, Robert ^b,c   Ogihara, Mitsunori ^d  

^a RUTGERS UNIVERSITY   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

^d University of Rochester   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR ALGEBRA; LINEAR EQUATIONS; COMPUTATIONAL METHODS; COMPUTER PROGRAMMING LANGUAGES; FUNCTIONS; INTEGER PROGRAMMING; MATRIX ALGEBRA; POLYNOMIALS; PROBABILITY;

INTEGER MATRICES; INTEGER SOLUTIONS; LOGSPACE; MATRIX RANK; NATURAL COMPLEXITY CLASS; SPAN PROGRAMS; SYSTEM OF LINEAR EQUATIONS; SYSTEMS OF LINEAR EQUATIONS;

MATRIX ALGEBRA; COMPUTATIONAL COMPLEXITY;

COUNTING HIERARCHY; EXACT COUNTING LOGSPACE HIERARCHY; FEASIBLE SYSTEMS; LOGSPACE REDUCTIONS; MATRIX RANK; NATURAL COMPLEXITY CLASSES;

EID: 0029723580     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/237814.237856     Document Type: Conference Paper

References (29)

1. E. Allender and M. Ogihara, Relationships among PL, #L, and the determinant Proc. 9th IEEE Structure in Complexity Theory Conference, 1994, pp. 267-278.
2. J. Balcázar, Adaptive logspace and depth-bounded reducibilities, Proc. 6th IEEE Structure in Complexity Theory Conference, 1991, pp. 240-254.
3. R. Beigel, personal communication.
4. J-Y Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, The Boolean Hierarchy I: Structural Properties, SIAM J. Comput. 17 (1988) 1232-1252.
5. J-Y Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, The Boolean Hierarchy II: Applications, SIAM J. Comput. 18 (1989) 95-111.
6. S. Cook, A taxonomy of problems with fast parallel algorithms, Information and Control 64 (1985) 2-22.
7. #L ?, Informatik-Preprint 8, Fachbereich Informatik der Humboldt-Universität zu Berlin, 1991.
8. S. Fenner, L. Fortnow, and S. Kurtz, Gap-definable counting classes, Journal of Computer and System Sciences 48 (1994) 116-148.
9. M. Furst, J. Saxe, and M. Sipser, Parity, circuits, and the polynomial-time hierarchy, Mathematical Systems Theory 17 (1984) 13-27.
10. J. von zur Gathen, Parallel linear algebra, in J. Reif, ed, Synthesis of Parallel Algorithms, Morgan Kaufmann, 1993, pp. 574-615.
11. M. Giesbrecht, Fast computation of the Smith normal form of an integer matrix, Proceedings ISS AC'95.
12. J. Gill, Computational complexity of probabilistic Turing machines, SIAM Journal on Computing 6 (1977) 675-695.
13. G. Gottlob, Collapsing Oracle-Tape Hierarchies, to appear in Proceedings of Complexity'96.
14. O. Ibarra, S. Moran, and L. Rosier, A note on the parallel complexity of computing the rank of order n matrices, Information Processing Letters 11 (1980) 162.
15. N. Immerman, Nondeterministic space is closed under complementation, SIAM J. Comput. 17 (1988) 935-938.
16. H. Jung, On probabilistic time and space, Proc. 12th ICALP, Lecture Notes in Computer Science 194, 1985, pp. 310-317.
17. E. Kaltofen, personal communication.
18. M. Karchmer, A. Wigderson, On Span Programs Proc. 8th IEEE Structure in Complexity Theory Conference, 1993, pp. 102-111.
19. N. Nisan and A. Ta-Shma, Symmetric logspace is closed under complement, STOC'95, pp. 140-146.
20. k-1 closures of NP and other classes, Information and Computation 120 (1995) 55-58.
21. M. Ogihara, The PL Hierarchy collapses, these proceedings.
22. W. Ruzzo, J. Simon, and M. Tompa, Spacebounded hierarchies and probabilistic computation, Journal of Computer and System Sciences 28 (1984) 216-230.
23. M. Santha and S. Tan, Verifying the determinant, Proc. COCOON'94, LNCS.
24. R. Szelepcsényi, The method of forced enumeration for nondeterministic automata, Acta Informatica 26 (1988) 279-284.
25. S. Toda, Counting problems computationally equivalent to the determinant, Technical Report CSIM 91-07, Dept. Comp. Sci. and Inf. Math., Univ. of Electro-Communications, Tokyo, 1991.
26. L. G. Valiant, Completeness classes in algebra, Proc. 11th ACM Symposium on the Theory of Computation, 1979, 249-261.
27. L. Valiant, Why is Boolean complexity theory difficult? in Boolean Function Complexity, edited by M. S. Paterson, London Mathematical Society Lecture Notes Series 169, Cambridge University Press, 1992.
28. V. Vinay, Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits, Proc. 6th IEEE Structure in Complexity Theory Conference (1991) 270-284.
29. K. Wagner, The complexity of combinatorial problems with succinct input representation, Acta Informatica 23 (1986) 325-356.