Nondeterministic NC1 Computation

Journal of Computer and System Sciences

Volumn 57, Issue 2, 1998, Pages 200-212

  Caussinus, Hervé ^a   McKenzie, Pierre ^a   Thérien, Denis ^b   Vollmer, Heribert ^c,d  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b MCGILL UNIVERSITY   (Canada)

^c UNIVERSITY OF WÜRZBURG   (Germany)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUIVALENCE CLASSES; FINITE AUTOMATA; MATHEMATICAL MODELS; POLYNOMIALS; SET THEORY;

COUNTING CLASSES; LEAF LANGUAGES;

COMPUTATIONAL COMPLEXITY;

EID: 0032180913     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1998.1588     Document Type: Article

References (39)

1. E. Allender, A note on uniform circuit lower bounds for the counting hierarchy, in "Proc. 2nd International Computing and Combinatorics Conference (COCOON)," Lecture Notes in Computer Science, Vol. 1090, pp. 127-135, Springer-Verlag, New York/Berlin, 1996.
2. E. Allender and M. Ogihara, Relationships among PL, #L, and the determinant, in "Proc. 9th Structure in Complexity Theory 1994," pp. 267-278.
3. 0, in "Proc. 8th Fundamentals of Computation Theory," Lecture Notes in Computer Science, Vol. 529, pp. 1-15, Springer-Verlag, New York/Berlin, 1991.
4. E. Allender and V. Gore, A uniform circuit lower bound for the permanent, SIAM J. Comput. 23 (1994), 1026-1049.
5. C. Alvarez and B. Jenner, A very hard log-space counting class, Theor. Comput. Sci. 107 (1993), 3-30.
6. 1, J. Comput. System Sci. 38 (1989), 150-164.
7. 1, J. Comput. System Sci. 41 (1990), 274-306.
8. 1, J. Assoc. Comput. Mach. 35(4) (1988), 941-952.
9. F. Bédard, F. Lemieux, and P. McKenzie, Extensions to Barrington's M-program model, Theor. Comput. Sci. A 107(1) (1993), 31-61.
10. R. Beigel, N. Reingold, and D. Spielman, PP is closed under intersection, in "Proc. 23rd Symposium on Theory of Computing, 1991," pp. 1-9.
11. M. Ben-Or and R. Cleve, Computing algebraic formulas using a constant number of registers, SIAM J. Comput. 21(1) (1992), 54-58.
12. A. Borodin, On relating time and space to size and depth, SIAM J. Comput. 64(4) (1977), 733-744.
13. D. Bovet, P. Crescenzi, and R. Silvestri, A uniform approach to define complexity classes, Theor. Comput. Sci. 104 (1992), 263-283.
14. H.-J. Burtschik, Comparing counting classes for logspace, one-way logspace, and first-order, in "Proc. 20th Symposium on Mathematical Foundations of Computer Science," Lecture Notes in Computer Science, Vol. 969, pp. 139-148, Springer-Verlag, New York/Berlin, 1995.
15. S. Buss, S. Cook, A. Gupta, and V. Ramachandran, An optimal parallel algorithm for formula evaluation, SIAM J. Comput. 21(4) (1992), 755-780.
16. P.-F. Dietz, I. Macarie, and J. Seiferas, Bits and relative order from residues, space efficiently, Inform. Process. Lett. 50(3) (1994), 123-127.
17. H. Caussinus, "Contributions à l'étude du non-déterminisme restreint," thèse de doctorat, Université de Montréal, 1996.
18. S. Fenner, L. Fortnow, and S. Kurtz, Gap-definable counting classes, J. Comput. System Sci. 48 (1994), 116-148.
19. U. Hertrampf, Complexity classes defined via k-valued logic, in "Proc. 9th Structure in Complexity Theory, 1994," pp. 224-234.
20. U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner, On the power of polynomial time bit-reductions, in "Proc. 8th Structure in Complexity Theory, 1993," pp. 200-207.
21. U. Hertrampf, H. Vollmer, and K. Wagner, On balanced vs. unbalanced computations trees, Math. Systems Theory, in press.
22. B. Jenner, P. McKenzie, and D. Thérien, Logspace and logtime leaf languages, in "Proc. 9th Structure in Complexity Theory, 1994," pp. 242-254.
23. J. Jiao, Some questions concerning circuit counting classes and other low level complexity classes, manuscript.
24. H. Jung, Depth efficient transformations of arithmetic into boolean circuits, in "Proc. Foundations of Computation Theory," Lecture Notes in Computer Science, Vol. 199, pp. 167-173, Springer-Verlag, New York/Berlin, 1985.
25. J. Köbler, U. Schöning, and J. Torán, On counting and approximation, Acta Inform. 26 (1989), 363-379.
26. K.-J. Lange, Unambiguity of circuits, Theor. Comput. Sci. 107 (1993), 77-94.
27. B. Litow, On iterated integer product, Inform. Process. Lett. 42 (1992), 269-272.
28. R. J. Lipton, and Y. Zalcstein, Word problems solvable in logspace, J. Assoc Comput. Mach. 24(3) (1977), 522-526.
29. I. Macarie, Space-efficient deterministic simulation of probabilistic automata, in "Proc. 11th Symposium on Theoretical Aspects of Computing (STACS)," Lecture Notes in Computer Science, Vol. 775, pp. 109-122, Springer-Verlag, New York/Berlin, 1994.
30. 1: The Automata-Theoretic Viewpoint, Comput. Complexity 1 (1991), 330-359.
31. W. Ruzzo, On uniform circuit complexity, J. Comput. System Sci. 23(3) (1981), 365-383.
32. S. Saluja, K. V. Subrahmanyam, and M. N. Thakur, Descriptive complexity of #P functions, in "Proc. 7th Structure in Complexity Theory, 1992," pp. 169-184.
33. S. Tan, Calcul et vérification parallèles de problèmes d'algèbre linéaire, thèse de doctorat, Université de Paris-Sud, U.F.R. Scientifique d'Orsay, No. d'ordre 3420, 1994.
34. S. Toda, Classes of arithmetic circuits capturing the complexity of computing the determinant, IEICE Trans. Commun./Electron./Inform. Systems E75-D (1992), 116-124.
35. L. Valiant, Completeness classes in algebra, in "Proc. 11th Symposium on Theory of Computing, 1979," pp. 249-261.
36. L. Valiant, The complexity of computing the permanent, Theor. Comput. Sci. 8 (1979), 189-201.
37. V. Vinay, Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits, in "Proc. 6th Structure in Complexity Theory, 1991," pp. 270-284.
38. H. Vollmer, and K. W. Wagner, Recursion theoretic characterizations of complexity classes of counting functions, Theor. Comput. Sci. 163 (1996), 245-258.
39. K. W. Wagner, Some observations on the connection between count-ing and recursion, Theor. Comput. Sci. 47 (1986), 131-147.