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- W1567779367 abstract "Recently Glaßer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question—whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P. The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all PSPACE-complete languages are polynomial-time length-decreasing self-reducible." @default.
- W1567779367 created "2016-06-24" @default.
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- W1567779367 date "2005-01-01" @default.
- W1567779367 modified "2023-09-26" @default.
- W1567779367 title "Separating the Notions of Self- and Autoreducibility" @default.
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- W1567779367 doi "https://doi.org/10.1007/11549345_27" @default.
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