Abstract
For any reduction r, a set is called “≤ pr -sparse” if it is ≤ pr -reducible to a sparse set. The difficulty of sets in nondeterministic complexity classes is investigated in terms of non-≤ p1−tt -sparseness, i.e., not being ≤ p1−tt -reducible to any sparse set. In particular, nondeterministic complexity classes used to specify various types of one-way functions are mainly considered, i.e., UP, N(poly), UBPP, and UP. For each such class, we prove that it contains a non-≤ p1−tt -sparse set unless it is included in P. Since these classes are included in more general nondeterministic complexity classes such as NP, easy consequences of our observations show the nonsparseness of ≤ p1−tt -hard sets for such classes.
(extended abstract)
This research was supported in part by the National Science Foundation under Grants CCR-8611980
Address as of August 1988: Dept. of Computer Science, Tokyo Institute of Technology, Tokyo 152, JAPAN
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Watanabe, O. (1988). On ≤ p1−tt -sparseness and nondeterministic complexity classes. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_151
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DOI: https://doi.org/10.1007/3-540-19488-6_151
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