Abstract
We study the autoreducibility and mitoticity of complete sets for NP and other complexity classes, where the main focus is on logspace reducibilities. In particular, we obtain:
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For NP and all other classes of the PH: Each \(\leq^{\rm log}_{\rm m}\)-complete set is \(\leq^{\rm log}_{\rm T}\)-autoreducible.
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For P, \(\Delta^p_k\), NEXP: Each \(\leq^{\rm log}_{\rm m}\)-complete set is a disjoint union of two \(\leq^{\rm log}_{\rm 2-tt}\)-complete sets.
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For PSPACE: Each \(\leq^{\rm p}_{\rm dtt}\)-complete set is a disjoint union of two \(\leq^{\rm p}_{\rm dtt}\)-complete sets.
Proofs omitted in this version can be found in the technical report [14].
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Glaßer, C., Witek, M. (2014). Autoreducibility and Mitoticity of Logspace-Complete Sets for NP and Other Classes. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_27
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