Monotonous and randomized reductions to sparse sets
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 30 (1996) no. 2, pp. 155-179.
@article{ITA_1996__30_2_155_0,
     author = {Arvind, V. and K\"obler, J. and Mundhenk, M.},
     title = {Monotonous and randomized reductions to sparse sets},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {155--179},
     publisher = {EDP-Sciences},
     volume = {30},
     number = {2},
     year = {1996},
     zbl = {0860.68051},
     mrnumber = {1420689},
     language = {en},
     url = {http://www.numdam.org/item/ITA_1996__30_2_155_0/}
}
TY  - JOUR
AU  - Arvind, V.
AU  - Köbler, J.
AU  - Mundhenk, M.
TI  - Monotonous and randomized reductions to sparse sets
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 1996
DA  - 1996///
SP  - 155
EP  - 179
VL  - 30
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/ITA_1996__30_2_155_0/
UR  - https://zbmath.org/?q=an%3A0860.68051
UR  - https://www.ams.org/mathscinet-getitem?mr=1420689
LA  - en
ID  - ITA_1996__30_2_155_0
ER  - 
Arvind, V.; Köbler, J.; Mundhenk, M. Monotonous and randomized reductions to sparse sets. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 30 (1996) no. 2, pp. 155-179. http://www.numdam.org/item/ITA_1996__30_2_155_0/

1. L. Dleman and K. Manders, Reducibility, randomness, and intractability, Proc. 9th ACM Symp. on Theory of Computing, 1977, pp. 151-163.

2. E. Allender, L. Hemachandra, M. Ogiwara and O. Watanabe, Relating equivalence and reducibility to sparse sets, SIAM Journal on Computing 1992, 21 (3), pp. 529-539. | MR 1163344 | Zbl 0761.68039

3. V. ArvindY. Han, L. A. Hemachandra, J. Kobler, A. Lozano, M. Mundhenk, M. Ogiwara, U. Schoning, R. Silvestri and T. Thierauf, Reductions to sets of low information content, In Complexity Theory, Current Research, Cambridge University Press, 1993, pp. 1-45. | MR 1255339 | Zbl 0794.68058

4. V. Arvind, J. Kobler and M. Mundhenk, On bounded truth-table, conjunctive, and randomized reductions to sparse sets, Proc. 12th Conf. FST & TCS, Lecture Notes in Computer Science, 52, pp. 140-151, Springer Verlag, 1992. | MR 1229096 | Zbl 0919.03034

5. V. Arvind, J. Kobler and M. Mundhenk, Upper bounds on the complexity of sparse and tally descriptions, Mathematical Systems Theory, to appear. | MR 1360197 | Zbl 0840.68041

6. J. Balcázar, Self-reducibility, Journal of Computer and System Sciences, 1990, 41, pp. 367-388. | MR 1079471 | Zbl 0718.68037

7. J. L. Balcázar, J. Díaz and J. Gabarró, Structural Complexity I, II. EATCS Monographs on Theoretical Computer Science, Springer Verlag, 1988. | MR 1047862 | Zbl 0638.68040

8. P. Berman, Relationship between density and deterministic complexity of NP-complete languages. Proceedings of the 5th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science, 62, pp. 63-71, Springer Verlag, 1978. | MR 520839 | Zbl 0382.68068

9. L. Berman and J. Hartmanis, On isomorphisms and density of NP and other complete sets, SIAM Journal on Computing, 1977, 6 (2), pp. 305-322. | MR 455536 | Zbl 0356.68059

10. R. Book and K. Ko, On sets truth-table reducible to sparse sets, SIAM Journal on Computing, 1988, 17 (5), pp. 903-919. | MR 961047 | Zbl 0665.68040

11. H. Buhrman, L. Longpré and E. Spaan, Sparse reduces conjunctively to tally, Proceedings of the 8th Structure in Complexity Theory Conference, IEEE Computer Society Press, 1993. | MR 1310802

12. R. Chang, J. Kadin and P. Rohatgi, Connections between the complexity of unique satisfiability and the threshold behavior of randomized reductions, Proceedings of the 6th Structure in Complexity Theory Conference, pp. 255-269, IEEE Computer Society Press, 1991.

13. S. Even, A. Selman and Y. Yacobi, The complexity of promise problems with applications to public-key cryptography, Information and Control, 1984, 61, pp. 114-133. | MR 772678 | Zbl 0592.94012

14. S. Fortune, A note on sparse complete sets, SIAM Journal on Computing, 1979, 8 (3), pp. 431-433. | MR 539260 | Zbl 0415.68006

15. R. Gavaldà and O. Watanabe, On the computational complexity of small descritpions, In Proceedings of the 6th Structure in Complexity Theory Conference, pp. 89-101. IEEE Computer Society Press, 1991, The final version is to appear in SIAM Journal on Computing. | Zbl 0799.68085

16. J. Gill, Computational complexity of probabilistic complexity classes, SIAM Journal on Computing, 1977, 6, pp. 675-695. | MR 464691 | Zbl 0366.02024

17. S. Homer and L. Longpré, On reductions of NP sets to sparse sets, Proc. 6th Structure in Complexity Theory Conference, pp. 79-88. IEEE Computer Society Press, 1991.

18. L. Hemachandra, M. Ogiwara and O. Watanabe, How hard are sparse sets? Proc. 7th Structure in Complexity Theory Conference, IEEE Computer Society Press, 1992. | MR 1249979

19. N. Immerman and S. Mahaney, Relativizing relativized computations, Theoretical Computer Science, 1989, 68, pp. 267-276. | MR 1031961 | Zbl 0679.68084

20. B. Jenner and J. Torán, Computing functions with parallel queries to NP, Proceedings of the 8th Structure in Complexity Theory Conference, pp. 280-291, IEEE Computer Society Press; May 1993. | MR 1310807

21. J. Kadin, PNP[log n] and sparse Turing-complete sets for NP, Journal of Computer and System Sciences, 1989, 39 (3) pp. 282-298. | MR 1030658 | Zbl 0693.68027

22. R. Karp and R. Lipton, Some connections between nonuniform and uniform complexity classes, Proceedings of the 12th ACM Symposium on Theory of Computing, 1980, pp. 302-309.

23. K. Ko, Some observations on the probabilistic algorithms and NP-hard problems, Information Processing Letters, 1982, 14, pp. 39-43. | MR 654074 | Zbl 0483.68045

24. K. Ko, On self-reducibility and weak p-selectivity, Journal of Computer and system Sciences, 1983, 26, pp. 209-221. | MR 708837 | Zbl 0519.68062

25. K. Ko, Distinguishing conjunctive and disjunctive reducibilities by sparse sets, Information and Computation, 1989, 81 (1) pp. 62-87. | MR 992304 | Zbl 0681.68066

26. J. Köbler, U. Schöning, S. Toda and J. Torán, Turing machines with few accepting computations and low sets for PP, Journal of Computer and System Sciences, 1992, 44 (2), pp. 272-286. | MR 1160464 | Zbl 0757.68056

27. R. Ladner, N. Lynch and A. Selman, A comparison of polynomial time reducibilities, Theoretical Computer Science, 1975, 1 (2), pp. 103-124. | MR 395319 | Zbl 0321.68039

28. S. Mahaney, Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis, Journal of Computer and System Sciences, 1982, 25 (2), pp. 130-143. | MR 680515 | Zbl 0493.68043

29. M. Mundhenk, Hausdorff-Reduktionen zu Mengen mit geringem Informationsgehalt, PhD dissertation, Universität Ulm, 1993.

30. M. Ogiwara and A. Lozano, On one query self-reducible sets, Theoretical Computer Science, 1993, 112, pp. 255-276. | MR 1216322

31. M. Ogiwara and O. Watanabe, On polynomial-time bounded truth-table reducibility of NP sets to sparse sets, SIAM Journal on Computing, 1991, 20(3), pp. 471-483. | MR 1094526 | Zbl 0741.68049

32. D. Ranjan and P. Rohatgi, Randomized reductions to sparse sets, Proceedings of the 7th Structure in Complexity Theory Conference, IEEE Computer Society Press, 1992, pp. 239-242. | MR 1249980

33. S. Saluja, Relativized limitations of the left set technique and closure classes of sparse sets, Proceedings of the 8th Structure in Complexity Theory Conference, pp. 215-222. IEEE Computer Society Press, 1993.

34. U. Schoning, On random reductions from sparse sets to tally sets, Information Processing Letters, 1993, 46, pp. 239-241. | Zbl 0780.68044

35. A. L. Selman, Reductions on NP and p-selective sets, Theoretical Computer Science, 1982, 19, pp. 287-304. | MR 671872 | Zbl 0489.03016

36. S. Tang and R. Book, Reducibilities on tally and sparse sets, Theoretical Informatics and Applications, 1991, 25, pp. 293-302. | Numdam | MR 1119046 | Zbl 0731.68039

37. S. Toda, On polynomial time truth-table reducibilities of intractable sets to P-selective sets, Mathematical Systems Theory, 1991, 24 (2), pp. 69-82. | MR 1096692 | Zbl 0722.68059

38. E. Ukkonen, TWO results on polynomial time truth-table reductions to sparse sets, SIAM Journal on Computing, 1983, 12 (3), pp. 580-587. | MR 707414 | Zbl 0532.68051

39. L. G. Valiant and V. V. Vazirani, NP is as easy as detecting unique solutions, Theoretical Computer Science, 1986 47, pp. 85-93. | MR 871466 | Zbl 0621.68030

40. K. W. Wagner, More complicated questions about maxima and minima, and some closures of NP, Theoretical Computer Science, 1987, 57, pp. 53-80. | MR 908480 | Zbl 0653.03027

41. C. Yap, Some consequences of non-uniform conditions on uniform classes, Theoretical Computer Science, 1983, 26, pp. 287-300. | MR 726923 | Zbl 0541.68017

42. Y. Yesha, On certain polynomial-time truth-table reducibilities of complete sets to sparse sets, SIAM Journal on Computing, 1983, 12 (3), pp. 411-425. | MR 707404 | Zbl 0545.03023