Abstract
Polynomial time oracle machines having restricted access to an oracle were studied e.g. in [LLS75, Wag90]. These restrictions — e.g. bounded number of queries, non-adaptive reductions — can be seen as syntactical restrictions, since one can recursively represent all the machines underlying these restrictions. In this paper, different kinds of semantically restricted polynomial time oracle machines are defined and investigated. It is shown that the strongest type of those machines w.r.t. NP oracles is the weakest w.r.t. sparse oracles.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
V. Arvind, J. Köbler, and M. Mundhenk. On bounded truth-table, conjunctive, and randomized reductions to sparse sets. In Proceedings 12th Conference on the Foundations of Software Technology & Theoretical Computer Science, pages 140–151. Lecture Notes in Computer Science #652, Springer-Verlag, 1992.
V. Arvind, J. Köbler, and M. Mundhenk. Upper bounds on the complexity of sparse and tally descriptions. Mathematical Systems Theory, 1995. to appear.
J.L. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I/II. EATCS Monographs on Theoretical Computer Science. Springer Verlag, 1988/1990.
H. Buhrman, L. Longpré, and E. Spaan. SPARSE reduces conjunctively to TALLY. In Proc. 8th Structure in Complexity Theory Conference, pages 208–214. IEEE, 1993.
S. Cook. The complexity of theorem proving procedures. In Proocedings of the 3rd ACM Symp. on Theory of Computing, pages 151–158, 1971.
R. Gavaldà and O. Watanabe. On the computational complexity of small descriptions. SIAM Journal on Computing, 1994. to appear.
L. Hemachandra, M. Ogiwara, and O. Watanabe. How hard are sparse sets? In Proc. 7th Structure in Complexity Theory Conference, 1992.
R. Karp. Reducibility among combinatorial problems. In R. Miller and J. Thatcher, editors, Complexity of Computer Computations, pages 85–104. Plenum Press, 1972.
K. Ko. Distinguishing conjunctive and disjunctive reducibilities by sparse sets. Information and Computation, 81(1):62–87, 1989.
R.E. Ladner, N.A. Lynch, and A.L. Selman. A comparison of polynomial time reducibilities. Theoretical Computer Science, 1:103–123, 1975.
A.L. Selman. Reductions on NP and p-selective sets. Theoretical Computer Science, 19:287–304, 1982.
K.W. Wagner. More complicated questions about maxima and minima, and some closures of NP. Theoretical Computer Science, 51:53–80, 1987.
K.W. Wagner. Bounded query classes. SIAM Journal on Computing, 19(5):833–846, 1990.
O. Watanabe. Polynomial time reducibility to a set of small density. In Proc. 1987 Structure in Complexity Theory Conference, pages 138–146. Lecture Notes in Computer Science, Springer-Verlag, 1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mundhenk, M. (1995). On monotonous oracle machines. In: Baeza-Yates, R., Goles, E., Poblete, P.V. (eds) LATIN '95: Theoretical Informatics. LATIN 1995. Lecture Notes in Computer Science, vol 911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59175-3_108
Download citation
DOI: https://doi.org/10.1007/3-540-59175-3_108
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59175-7
Online ISBN: 978-3-540-49220-7
eBook Packages: Springer Book Archive