Abstract
We show that the complexity-theoretic notion of almost-everywhere complex functions is identical to the recursion-theoretic notion of bi-immune sets in the nondeterministic space domain. Furthermore we derive a very strong separation theorem for nondeterministic space — witnessing this fact by almost-everywhere complex sets — that is equivalent to the traditional infinitely-often complex hierarchy result. The almost-everywhere complex sets constructed here are the first such sets constructed for nondeterministic complexity classes.
This author was supported in part by the National Science Foundation under grant CCR 8811996.
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E. Allender, R. Beigel, U. Hertrampf, and S. Homer. A note on the almost-everywhere hierarchy for nondeterministic time. To appear in STACS 90, Lecture Notes in Computer Science.
J.L. Balcázar and U. Schöning. Bi-immune sets for complexity classes. Mathematical Systems Theory, 18(1):1–10, 1985.
L. Berman. On the structure of complete sets: almost everywhere complexity and infinitely often speedup. In Proc. 17th IEEE Symposium on the Foundations of Computer Science, volume 17, pages 76–80, 1976.
J.G. Geske. On the structure of intractable sets. PhD thesis, Iowa State University, 1987.
J.G. Geske, D. Huynh, and J. Seiferas. A technical note on bi-immunity and almost everywhere complexity. To appear in Information and Computation.
J.G. Geske, D. Huynh, and A. Selman. A hierarchy theorem for almost everywhere complex sets with application to polynomial complexity degrees. In STACS 87, Lecture Notes in Computer Science Vol. 247, pp. 125–135. Springer-Verlag, Berlin, 1987.
O.H. Ibarra. A note concerning nondeterministic tape complexities. Journal of the ACM, 19:608–612, 1972.
N. Immerman. Nondeterministic space is closed under complement. In Proc. Structure in Complexity Theory, volume 3, pages 112–115, 1988.
A.R. Meyer and E.M. McCreight. Computationally complex and pseudo-random zero-one valued functions. In Z. Kohavi and A. Paz, editors, Theory of Machines and Computations, pp. 19–42. Academic Press, New York, 1971.
M.O. Rabin. Degree of difficulty of computing a function and a partial ordering of recursive sets. Technical Report 2, Hebrew University, Jerusalem, Israel, 1960.
J.I. Seiferas, M.J. Fischer, and A.R. Meyer. Separating nondeterministic time complexity classes. Journal of the ACM, 25:146–167, 1978.
R. Szelepcesényi. The method of forcing for nondeterministic automata. Bull. European Association Theoretical Computer Science, pages 96–100, 1987.
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© 1991 Springer-Verlag Berlin Heidelberg
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Geske, J.G., Kakihara, D. (1991). Almost-everywhere complexity, bi-immunity and nondeterministic space. In: Akl, S.G., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '90. ICCI 1990. Lecture Notes in Computer Science, vol 468. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53504-7_60
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DOI: https://doi.org/10.1007/3-540-53504-7_60
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