Abstract
We investigate the diagonalization theorems in [7] (Theorem 23), [3] (Theorem 6) and [10] (main Theorem) and show that they can be strengthened so as to be applicable to most complexity classes, not just to those closed under polynomial-time reducibility. Thus the applications in [7], [3] and [10] (e.g. P ≠ P ⇒ NP\P is not recursively presentable) are not peculiar to P, NP, PSPACE etc.; rather, they are examples of properties common to almost all "reasonable" complexity classes.
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References
T.P. Baker and A.L. Selman, A second step toward the polynomial hierarchy, Theor. Comput. Sci. 8 (1979) 177–187.
J.L. Balcazar and J. Diaz, A note on a theorem by Ladner, Information Processing Lett. 15 (1982) 84–86.
P. Chew and M. Machtey, A note on structure and looking back applied to the relative complexity of computable functions, J. Comput. System Sci. 22 (1981) 53–59.
J.E. Hopcroft and J.D. Ullman, Some results on tape-bounded Turing machines, J. ACM 16 (1969) 168–177.
R.E. Ladner, On the structure of polynomial time reducibility, J. ACM 22 (1975) 155–171.
R.E. Ladner, N.A. Lynch and A.L. Selman, A comparison of polynomial time reducibilities, Theor. Comput. Sci 1 (1975) 103–123.
L.H. Landweber, R.J. Lipton & E.L. Robertson, On the structure of sets in NP and other complexity classes, Theoret. Comput. Sci. 15 (1981) 181–200.
T.J. Long, Strong nondeterministic polynomial-time reducibilities, Theoret. Comput. Sci. 21 (1982) 1–25.
K. Regan, On diagonalization methods and the structure of language classes, Proceedings of the 1983 FCT-Conference, Springer 1983, 368–380.
U. Schöning, A uniform approach to obtain diagonal sets in complexity classes, Theoret. Comput. Sci. 18 (1982), 95–103.
U. Schöning, On the structure of Δ p2 , Information Processing Lett. 16 (1983), 209–211.
C. Wrathall, Complete sets and the polynomial-time hierarchy, Theoret. Comput. Sci. 3 (1977) 23–33.
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© 1984 Springer-Verlag Berlin Heidelberg
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Schmidt, D. (1984). On the complement of one complexity class in another. In: Börger, E., Hasenjaeger, G., Rödding, D. (eds) Logic and Machines: Decision Problems and Complexity. LaM 1983. Lecture Notes in Computer Science, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13331-3_34
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DOI: https://doi.org/10.1007/3-540-13331-3_34
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