Abstract
We discuss some differences between p-generic and strongly p-generic sets. While the class of p-generic sets has measure 1, the class of strongly p-generic sets has measure 0 in an appropriate measure space. Also contrasting the situation with the p-generic sets, for no oracle A, NP(A) contains a strongly p-generic set. Moreover, the notion of np-genericity is introduced and strong p-genericity is shown to be even stronger than np-genericity.
Preview
Unable to display preview. Download preview PDF.
References
Ambos-Spies, K., Fleischhack, H., and Huwig, H., P-generic sets, in "Automata, Languages and Programming", LNCS 172 (1984), 58–68.
Ambos-Spies, K.,Fleischhack, H., and Huwig, H., Diagonalizations over polynomial time computable sets, Forschungsbericht Nr. 177 (1984), Abteilung Informatik, Universität Dortmund.
Ambos-Spies, K., P-mitotic sets, in "Logic and machines: Decision problems and complexity", LNCS 171 (1984), 1–23.
Bennet, C., and Gill, J., Relative to a random oracle A, pA ≠ NPA ≠ co-NPA with probability 1, SIAM J. Comp. 10 (1981), 96–113.
Fleischhack, H., On diagonalizations over complexity classes, Dissertation, Dortmund 1985.
Halmos, P., Measure Theory, Springer, New York, 1950.
Homer, S., and Maass, W., Oracle dependent properties of the lattice of NP-sets, TCS 24 (1983), 279–289.
Jockusch, C., Notes on genericity for r. e. sets, unpublished, 1983.
Maass, W., Recursively enumerable generic sets, JSL (1982), 809–823.
Mehlhorn, K., On the size of sets of computable functions, Techn. Rep. 72–164, Ithaca, New York, 1973.
Mehlhorn, K., The ‘almost all’ theory of subrecursive degrees is decidable, Tech. Rep. 73–170, Ithaca, New York, 1973.
Selman, A., P-selective sets, tally languages and the behaviour of polynomial time reducibilities on NP, Math. Systems Theory 13 (1979), 55–65.
Willard, S., General topology, Addison-Wesley, Reading, Mass., 1970.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fleischhack, H. (1986). P-genericity and strong p-genericity. In: Gruska, J., Rovan, B., Wiedermann, J. (eds) Mathematical Foundations of Computer Science 1986. MFCS 1986. Lecture Notes in Computer Science, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016258
Download citation
DOI: https://doi.org/10.1007/BFb0016258
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16783-9
Online ISBN: 978-3-540-39909-4
eBook Packages: Springer Book Archive