Space-efficient informational redundancy

AbstractWe study the relation of autoreducibility and mitoticity for polylog-space many-one reductions and log-space many-one reductions. For polylog-space these notions coincide, while proving the same for log-space is out of reach. More precisely, we show the following results with respect to nontrivial sets and many-one reductions:1.polylog-space autoreducible ⇔ polylog-space mitotic,2.log-space mitotic ⇒ log-space autoreducible ⇒ (logn⋅loglogn)-space mitotic,3.relative to an oracle, log-space autoreducible ⇏ log-space mitotic. The oracle is an infinite family of graphs whose construction combines arguments from Ramsey theory and Kolmogorov complexity

Autoreducibility of NP-Complete Sets

We study the polynomial-time autoreducibility of NP-complete sets and obtain separations under strong hypotheses for NP. Assuming there is a p-generic set in NP, we show the following: - For every $k \geq 2$, there is a $k$-T-complete set for NP that is $k$-T autoreducible, but is not $k$-tt autoreducible or $(k-1)$-T autoreducible. - For every $k \geq 3$, there is a $k$-tt-complete set for NP that is $k$-tt autoreducible, but is not $(k-1)$-tt autoreducible or $(k-2)$-T autoreducible. - There is a tt-complete set for NP that is tt-autoreducible, but is not btt-autoreducible. Under the stronger assumption that there is a p-generic set in NP $\cap$ coNP, we show: - For every $k \geq 2$, there is a $k$-tt-complete set for NP that is $k$-tt autoreducible, but is not $(k-1)$-T autoreducible. Our proofs are based on constructions from separating NP-completeness notions. For example, the construction of a 2-T-complete set for NP that is not 2-tt-complete also separates 2-T-autoreducibility from 2-tt-autoreducibility

Dagstuhl News January - December 2007

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic