Question: [32] The method using resource-bounded Kolmogorov complexity to construct oracles in Section 7.3.1 can be used to obtain many more oracles. Define Notice that EXPTIME
[32] The method using resource-bounded Kolmogorov complexity to construct oracles in Section 7.3.1 can be used to obtain many more oracles. Define
![EXPTIME=DTIME[2"]. CEN](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1733/3/1/2/41067503f9a040591733312409715.jpg){kind=small}
Notice that EXPTIME is different from the class E. Let NPSPACE stand for the nondeterministic version of PSPACE. Let us consider oracle Turing machines with an unbounded oracle tape. Prove the following:
(a) There is an oracle A such that NPSPACEA ⊂ EXPTIMEA.
(b) There is an oracle B such that PSPACEB ⊂ EXPTIMEB, where the containment is proper.
(c) There is an oracle C such that EXPTIMEC ⊂ NPSPACEC .
(d) There is an oracle D with PSPACED ⊂ NPSPACED = EXPTIMED, where the containment is proper.
Comments. Item
(d) implies that Savitch’s theorem [W.J. Savitch, J.
Comput. System Sci. 4:2(1972), 177–192] does not relativize with an unbounded oracle tape. Source: [R. Gavald`a, L. Torenvliet, O. Watanabe, and J.L. Balc´azar, Proc. 15th Math. Found. Comput. Sci. Conf., 1991, pp. 269–276]. For a comprehensive study in this direction, see [R.
Gavald`a, Ph.D. thesis, Universitat Polit´ecnica de Catalunya, 1992].
EXPTIME=DTIME[2"]. CEN
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