Abstract | ||
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We investigate the autoreducibility and mitoticity of complete sets for several classes with respect to different polynomial-time and logarithmic-space reducibility notions. Previous work in this area focused on polynomial-time reducibility notions. Here we obtain new mitoticity and autoreducibility results for the classes EXP and NEXP with respect to some restricted truth-table reductions (e.g., $\leq^{p}_{2-tt},\leq^{p}_{ctt},\leq^{p}_{dtt}$). Moreover, we start a systematic study of logarithmic-space autoreducibility and mitoticity which enables us to also consider P and smaller classes. Among others, we obtain the following results: · Regarding $\leq^{log}_{m}, \leq^{log}_{2-tt}, \leq^{log}_{dtt}$ and $\leq^{log}_{ctt}$, complete sets for PSPACE and EXP are mitotic, and complete sets for NEXP are autoreducible. · All $\leq^{log}_{1-tt}$-complete sets for NL and P are $\leq^{log}_{2-tt}$-autoreducible, and all $\leq^{log}_{btt}$-complete sets for NL, P and $\Delta^{p}_{k}$ are $\leq^{log}_{log-T}$-autoreducible. · There is a $\leq^{log}_{3-tt}$-complete set for PSPACE that is not even $\leq^{log}_{btt}$-autoreducible. Using the last result, we conclude that some of our results are hard or even impossible to improve. |
Year | DOI | Venue |
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2013 | 10.1007/978-3-642-39206-1_40 | ICALP |
Keywords | DocType | Volume |
polynomial-time reducibility notion,last result,new mitoticity,logarithmic-space autoreducibility,classes exp,complete set,polynomial-time reduction,following result,autoreducibility result,different polynomial-time,logarithmic-space reducibility notion | Journal | 20 |
ISSN | Citations | PageRank |
0302-9743 | 4 | 0.47 |
References | Authors | |
7 | 5 |
Name | Order | Citations | PageRank |
---|---|---|---|
Christian Glaßer | 1 | 175 | 24.52 |
Dung T. Nguyen | 2 | 134 | 10.29 |
Christian Reitwießner | 3 | 39 | 4.81 |
Alan L. Selman | 4 | 1532 | 185.40 |
Maximilian Witek | 5 | 25 | 3.71 |