Abstract
The notion of a robust oracle machine and an oracle set "helping" a robust oracle machine has been introduced for better understanding the nondeterministic "witness searching" process in NP problems. It is shown that straightforward modifications of the original notion are closely related with other concepts in structural complexity theory, such as "self-reducibility", "lowness", and "interactive proof systems".
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
M. Abadi, J. Feigenbaum and J. Kilian, On hiding information from an oracle, Proc. 19th ACM STOC 1987, 195–203.
L. Adleman and K. Manders, Reducibility, randomness, and intractability, Proc. 9th ACM STOC, 1977, 151–163.
L. Babai, Trading group theory for randomness, Proc. 17th ACM STOC, 1985, 421–429.
J.L. Balcázar, Self-reducibility, Proc. 4th STACS, Lecture Notes in Computer Science 247, 136–147, Springer, 1985.
J.L. Balcázar, R.V. Book and U. Schöning, Sparse sets, lowness and highness, Proc. MFCS 1984, Lect. Notes in Comput. Sci. 176, 185–193. See also: SIAM Journal on Computing 15 (1986), 739–747.
J.L. Balcázar, J. Diaz and J. Gabarro, Structural Complexity I, EATCS Monographs on Theor. Comput. Sci., Vol. 11, Springer, 1988.
R.B. Boppana, J. Hastad and S. Zachos, Does co-NP have short interactive proofs?, Inform. Proc. Letters 25 (1987), 127–132.
L. Fortnow, J. Rompel and M. Sipser, On the power of multi-prover interactive protocols, 3rd Structure in Complexity Theory Conf., IEEE Comp. Society, 1988.
R. Gavaldá and J.L. Balcázar, Strong and robustly strong polynomial time reducibilities to sparse sets, manuscript, 1988.
J. Gill, Computational complexity of probabilistic complexity classes, SIAM Journal on Computing 6 (1977), 675–695.
S. Goldwasser, S. Micali and C. Rackoff, The knowledge complexity of interactive proof systems, Proc. 17th ACM STOC 1985, 291–304.
O. Goldreich, S. Micali and A. Wigderson, Proofs that relase minimum knowledge, Proc. MFCS 1986, Lecture Notes in Comput. Sci. 233, 639–650, Springer, 1986. Also: Proofs that yield nothing but their validity and a methodology of interactive proof systems, Proc. 17th ACM STOC 1985, 291–304.
S. Goldwasser and M. Sipser, Private coins versus public coins in interactive proof systems, 18th ACM STOC 1986, 59–68.
J. Hartmanis, On sparse sets in NP — P, Inform. Proc. Letters 16 (1983), 55–60.
J. Hartmanis and L.A. Hemachandra, One-way functions, robustness, and non-isomorphism of NP-complete sets, Proc. 2nd Structure in Complexity Theory Conf., IEEE Computer Society, 1987, 160–174.
J. Kämper, Non-uniform proof systems: a new framework to describe non-uniform and probabilistic complexity classes, Univ. Oldenburg, Techn. Report 3/87.
K. Ko, On helping by robust oracle machines, Proc. 2nd Structure in Complexity Theory Conf., IEEE Computer Society, 1987, 182–190. Also: Theoret. Comput. Sci. 52 (1987), 15–36.
K. Ko, On self-reducibility and weak p-selectivity, Journal of Computer and System Sciences 26 (1983), 209–221.
K. Ko and U. Schöning, On circuit-size complexity and the low hierarchy in NP, SIAM Journ. on Computing 14 (1985), 41–51.
C. Lautemann, BPP and the polynomial hierachy, Inform. Proc. Letters 17 (1983), 215–217.
T. Long, Strong nondeterministic polynomial-time reducibilities, Theor. Comput. Sci. 21 (1982), 1–25.
A. Meyer and M. Paterson, Whith what frequency are apparently intractable problems difficult?, Techn. Report 126, MIT, 1979.
U. Schöning, Complexity and Structure, Lecture Notes in Comput. Sci. 211, Springer, 1985.
U. Schöning, Robust algorithms: a different approach to oracles, Proc. ICALP 84, Lecture Notes in Computer Science 172, 448–453, 1984. Also: Theor. Comput. Sci. 40 (1985), 57–66.
U. Schöning, Graph isomorphism is in the low hierarchy, Proc. STACS 87, Lect. Notes in Comput. Sci. 247, 114–124, Springer, 1987. (to appear in JCSS)
U. Schöning, Probabilistic complexity classes and lowness, Proc. 2nd Structure in Complexity Theory Conf., IEEE Computer Society, 1987, 2–8.
U. Schöning, A low and a high hierarchy within NP, Journ. of Comput. Syst. Sci. 27 (1983), 14–28.
U. Schöning, Netzwerkkomplexität, probabilistische Algorithmen und Relativierungen, Habilitationsschrift, Univ. Stuttgart, 1985.
C.P. Schnorr, Optimal algorithms for self-reducible problems, Proc. 3rd ICALP 76, Edinburgh University Press 1976, 322–337.
M. Sipser, A complexity theoretic approach to randomness, Proc. 15th ACM STOC 1983, 330–335.
J. Torán, personal communication, 1987.
M. Tompa and H. Woll, Random self-reducibility and zero knowledge interactive proofs of possession of information, Proc. 28th FOCS 87, IEEE Computer Soc., 1987, 472–482.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schöning, U. (1988). Robust oracle machines. In: Chytil, M.P., Koubek, V., Janiga, L. (eds) Mathematical Foundations of Computer Science 1988. MFCS 1988. Lecture Notes in Computer Science, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017134
Download citation
DOI: https://doi.org/10.1007/BFb0017134
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50110-7
Online ISBN: 978-3-540-45926-2
eBook Packages: Springer Book Archive