Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Complete problems and strong polynomial reducibilities
SIAM Journal on Computing
On 1-truth-table-hard languages
Theoretical Computer Science
On being incoherent without being very hard
Computational Complexity
Separating Complexity Classes Using Autoreducibility
SIAM Journal on Computing
Polynomial reducibilities and complete sets.
Polynomial reducibilities and complete sets.
The cpa's responsibility for the prevention and detection of computer fraud.
The cpa's responsibility for the prevention and detection of computer fraud.
Autoreducibility, mitoticity, and immunity
Journal of Computer and System Sciences
SIAM Journal on Computing
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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.