@article{ITA_1996__30_1_1_0, author = {Allender, Eric and Ogihara, Mitsunori}, title = {Relationships among $PL$, $\#L$, and the determinant}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {1--21}, publisher = {EDP-Sciences}, volume = {30}, number = {1}, year = {1996}, mrnumber = {1398856}, zbl = {0851.68033}, language = {en}, url = {http://www.numdam.org/item/ITA_1996__30_1_1_0/} }
TY - JOUR AU - Allender, Eric AU - Ogihara, Mitsunori TI - Relationships among $PL$, $\#L$, and the determinant JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 1996 SP - 1 EP - 21 VL - 30 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/item/ITA_1996__30_1_1_0/ LA - en ID - ITA_1996__30_1_1_0 ER -
%0 Journal Article %A Allender, Eric %A Ogihara, Mitsunori %T Relationships among $PL$, $\#L$, and the determinant %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 1996 %P 1-21 %V 30 %N 1 %I EDP-Sciences %U http://www.numdam.org/item/ITA_1996__30_1_1_0/ %G en %F ITA_1996__30_1_1_0
Allender, Eric; Ogihara, Mitsunori. Relationships among $PL$, $\#L$, and the determinant. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 30 (1996) no. 1, pp. 1-21. http://www.numdam.org/item/ITA_1996__30_1_1_0/
1. Oracles vs Proof techniques that do not relativize, Proc. SIGAL International Symposium on Algorithms, Lecture Notes in Computer Science, 1990, 450, pp. 39-52. | MR
,2. The complexity of matrix rank and feasible systems of linear equations, to appear in Proc. 28th STOC, 1996. | MR | Zbl
, and ,3. Depth reduction for noncommutative arithmetic circuits, Proc. 25th STOC, 1993, pp. 515-522.
and ,4. Adaptive logspace reducibility and parallel time, Mathematical Systems Theory, 1995, 28, pp. 117-140. | MR | Zbl
, and ,5. A very hard log-space counting class, Theoretical Computer Science, 1993, 107, pp. 3-30. | MR | Zbl
and ,6. Adaptive logspace and depth-bounded reducibilities, Proc. 6th IEEE Structure in Complexity Theory Conference, 1991, pp. 240-254.
,7. On computing the determinant in small parallel time using a small number of processors, Information Processing Letters, 1984, 18, pp. 147-150. | MR | Zbl
,8. Parallel computation for well-endowed rings and space-bounded probabilistic machines, Information and Control, 1983, 48, pp. 113-136. | MR | Zbl
, and ,9. Two applications of inductive counting for complementation problems, SIAM Journal on Computing, 1989, 18, pp. 559-578. | MR | Zbl
, , , and ,10. An optimal parallel algorithm for formula evaluation, SIAM Journal on Computing, 1992, 21, pp. 755-780. | MR | Zbl
, , and ,11. Zero-one permanent is #P-complete, a simpler proof, Proc. 2nd Israel Symposium on Theory of Computing and Systems (ISTCS93), IEEE press.
and ,12. On uniformity within NC1, Journal of Computer and System Sciences, 1990, 41, pp. 274-306. | MR | Zbl
, and ,13. PP is closed under intersection, Journal of Computer and System Sciences, 1995, 50, pp. 191-202. | MR | Zbl
, and ,14. Structure and Importance of Logspace MOD-Classes, Mathematical Systems Theory, 1992, 25, pp. 223-237. | MR | Zbl
, , and ,15. A taxonomy of problems with fast parallel algorithms, Information and Control, 1985, 64, pp. 2-22. | MR | Zbl
,16. DET = L#L?, Informatik-Preprint 8, Fachbereich Informatik der Humboldt-Universität zu Berlin, 1991.
,17. Gap-definable counting classes, Journal of Computer and System Sciences, 1994, 48, pp. 116-148. | MR | Zbl
, and ,18. PP is closed under truth-table reductions, Proc. 6th IEEE Structure in Complexity Theory Conference, 1991, pp. 13-15. | Zbl
and ,19. Computational complexity of probabilistic Turing machines, SIAM Journal on Computing, 1977, 6, pp. 675-695. | MR | Zbl
,20. Deterministic simulation of tape-bounded probabilistic Turing machine transducers, Theoretical Computer Science, 1980, 12, pp. 333-338. | MR | Zbl
, and ,21. The power of the middle bit of a #P function, to appear in Journal of Computer and System Sciences. | MR | Zbl
, , , and ,22. The power of witness reduction, to appear in SIAM Journal on Computing. A preliminary version appeared in Proc. 6th IEEE Structure in Complexity Theory Conference, 1991, pp. 43-59.
,23. Markov Chains, Theory and Applications, Wiley and Sons, 1976. | MR | Zbl
and ,24.
, personal communication.25. Relationships between probabilistic and deterministic tape complexity, Proc. 10th MFCS, Lecture Notes in Computer Science, 1981, 118, pp. 339-346. | MR | Zbl
,26. On probabilistic tape complexity and fast circuits for matrix inversion problems, Proc, 11th ICALP, Lecture Notes in Computer Science, 1984, 172, pp. 281-291. | MR | Zbl
,27. On probabilistic time and space, Proc. 12th ICALP, Lecture Notes in Computer Science, 1985, 194, pp. 310-317. | MR | Zbl
,28. Stochastische Turingmaschinen und die Kompliziertheit arithmetischer Probleme, doctoral dissertation, Humboldt-Universität, East Berlin.
,29. Relativization of questions about log space computability, Mathematical Systems Theory, 1976, 10, pp. 19-32. | MR | Zbl
and ,30. A comparison of polynomial-time reducibilities, Theoretical Computer Science, 1975, 1, pp. 103-123. | MR | Zbl
, and ,31. Space-efficient deterministic simulation of probabilistic automata, Proc. 11th STACS, Lecture Notes in Computer Science, 1994, 775, pp. 109-122.
,32. Space-bounded probabilistic computation: old and new stories, SIGACT News Complexity Theory Column 10 (edited by Lane Hemaspaandra), SIGACT News, 1995, 26, number 3, September, pp. 2-12.
,33. RL ⊆ SC, Computational Complexity, 1994, 4, pp. 1-11. | MR | Zbl
,34. NCk(NP) = ACk-1(NP), Proc. 11th STACS, Lecture Notes in Computer Science, 1994, 775, pp. 313-324. | MR
,35. The PL Hierarchy collapses, to appear in Proc. 28th STOC, 1996. | MR
,36. A complexity theory for feasible closure properties, Journal of Computer and System Sciences, 1993, 46, pp. 295-325. | MR | Zbl
and ,37. On the power of one bit of a #P-function, Proc. 4th Italian Conference on Theoretical Computer Science, World Scientific Press, Singapore, 1992, pp. 317-329. See also [21]. | MR
and ,38.
, personal communication.39. Space-bounded hierarchies and probabilistic computation, Journal of Computer and System Sciences, 1984, 28, pp. 216-230. | MR | Zbl
, and ,40. A note on the permanent problem, Information Processing Letters, 1992, 43, pp. 1-5. | MR | Zbl
,41. On tape-bounded probabilistic Turing machine acceptors, Theoretical Computer Science, 1981, 16, pp. 158-167. | MR | Zbl
,42. Space-bounded probabilistic Turing machine complexity classes are closed under complement, Proc. 13th STOC, 1981, pp. 158-167.
,43. On tape-bounded probabilistic Turing machine transducers, Proc. 19th FOCS, 1978, pp. 107-112.
, and ,44. Counting problems computationally equivalent to the determinant, Technical Report CSIM 91-07, Dept. Comp. Sci. and Inf. Math., Univ. of Electro-Communications, Tokyo, 1991.
,45. Classes of arithmetic circuits capturing the complexity of computing the determinant, IEICE Trans. Inf. and Syst., 1992, vol. E75-D, pp. 116-124.
,46. Complexity classes defined by counting quantifiers, Journal of the ACM, 1991, 38, pp. 753-774. | MR | Zbl
,47. The complexity of computing the Permanent, Theoretical Computer Science, 1979, 8, pp. 189-201. | MR | Zbl
,48. 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. | MR | Zbl
,49. Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits, Proc. 6th IEEE Structure in Complexity Theory Conference, 1991, pp. 270-284.
,50. The complexity of combinatorial problems with succinct input representation, Acta Informatica, 1986, 23, pp. 325-356. | MR | Zbl
,51. Relativized NC, Mathematical Systems Theory, 1987, 20, pp. 13-29. | MR | Zbl
,52. Decomposing NC and AC, SIAM Journal on Computing, 1990, 19, pp. 384-396. | MR | Zbl
,53. #P-completeness via many-one reductions, International Journal of Foundations of Computer Science, 1991, 2, pp. 77-82. | MR | Zbl
,54.
, personal communication.