Monotonous and randomized reductions to sparse sets

 Access to full text

 Full (PDF)

1. 1. L. DLEMAN and K. MANDERS, Reducibility, randomness, and intractability, Proc. 9th ACM Symp. on Theory of Computing, 1977, pp. 151-163. 
2. 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. Zbl0761.68039MR1163344
3. 3. V. ARVIND Y. 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. Zbl0794.68058MR1255339
4. 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. Zbl0919.03034MR1229096
5. 5. V. ARVIND, J. KOBLER and M. MUNDHENK, Upper bounds on the complexity of sparse and tally descriptions, Mathematical Systems Theory, to appear. Zbl0840.68041MR1360197
6. 6. J. BALCÁZAR, Self-reducibility, Journal of Computer and System Sciences, 1990, 41, pp. 367-388. Zbl0718.68037MR1079471
7. 7. J. L. BALCÁZAR, J. DÍAZ and J. GABARRÓ, Structural Complexity I, II. EATCS Monographs on Theoretical Computer Science, Springer Verlag, 1988. Zbl0638.68040MR1047862
8. 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. Zbl0382.68068MR520839
9. 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. Zbl0356.68059MR455536
10. 10. R. BOOK and K. KO, On sets truth-table reducible to sparse sets, SIAM Journal on Computing, 1988, 17 (5), pp. 903-919. Zbl0665.68040MR961047
11. 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. Zbl0830.68042MR1310802
12. 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. Zbl0837.68026
13. 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. Zbl0592.94012MR772678
14. 14. S. FORTUNE, A note on sparse complete sets, SIAM Journal on Computing, 1979, 8 (3), pp. 431-433. Zbl0415.68006MR539260
15. 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. Zbl0799.68085
16. 16. J. GILL, Computational complexity of probabilistic complexity classes, SIAM Journal on Computing, 1977, 6, pp. 675-695. Zbl0366.02024MR464691
17. 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. Zbl0806.68046
18. 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. Zbl0761.68039MR1249979
19. 19. N. IMMERMAN and S. MAHANEY, Relativizing relativized computations, Theoretical Computer Science, 1989, 68, pp. 267-276. Zbl0679.68084MR1031961
20. 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. Zbl0873.68058MR1310807
21. 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. Zbl0693.68027MR1030658
22. 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. 23. K. KO, Some observations on the probabilistic algorithms and NP-hard problems, Information Processing Letters, 1982, 14, pp. 39-43. Zbl0483.68045MR654074
24. 24. K. KO, On self-reducibility and weak p-selectivity, Journal of Computer and system Sciences, 1983, 26, pp. 209-221. Zbl0519.68062MR708837
25. 25. K. KO, Distinguishing conjunctive and disjunctive reducibilities by sparse sets, Information and Computation, 1989, 81 (1) pp. 62-87. Zbl0681.68066MR992304
26. 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. Zbl0757.68056MR1160464
27. 27. R. LADNER, N. LYNCH and A. SELMAN, A comparison of polynomial time reducibilities, Theoretical Computer Science, 1975, 1 (2), pp. 103-124. Zbl0321.68039MR395319
28. 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. Zbl0493.68043MR680515
29. 29. M. MUNDHENK, Hausdorff-Reduktionen zu Mengen mit geringem Informationsgehalt, PhD dissertation, Universität Ulm, 1993. 
30. 30. M. OGIWARA and A. LOZANO, On one query self-reducible sets, Theoretical Computer Science, 1993, 112, pp. 255-276. Zbl0780.68043MR1216322
31. 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. Zbl0741.68049MR1094526
32. 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. MR1249980
33. 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. 34. U. SCHONING, On random reductions from sparse sets to tally sets, Information Processing Letters, 1993, 46, pp. 239-241. Zbl0780.68044
35. 35. A. L. SELMAN, Reductions on NP and p-selective sets, Theoretical Computer Science, 1982, 19, pp. 287-304. Zbl0489.03016MR671872
36. 36. S. TANG and R. BOOK, Reducibilities on tally and sparse sets, Theoretical Informatics and Applications, 1991, 25, pp. 293-302. Zbl0731.68039MR1119046
37. 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. Zbl0722.68059MR1096692
38. 38. E. UKKONEN, TWO results on polynomial time truth-table reductions to sparse sets, SIAM Journal on Computing, 1983, 12 (3), pp. 580-587. Zbl0532.68051MR707414
39. 39. L. G. VALIANT and V. V. VAZIRANI, NP is as easy as detecting unique solutions, Theoretical Computer Science, 1986 47, pp. 85-93. Zbl0621.68030MR871466
40. 40. K. W. WAGNER, More complicated questions about maxima and minima, and some closures of NP, Theoretical Computer Science, 1987, 57, pp. 53-80. Zbl0653.03027MR908480
41. 41. C. YAP, Some consequences of non-uniform conditions on uniform classes, Theoretical Computer Science, 1983, 26, pp. 287-300. Zbl0541.68017MR726923
42. 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. Zbl0545.03023MR707404