TY - GEN
T1 - Gap MCSP Is Not (Levin) NP-Complete in Obfustopia
AU - Mazor, Noam
AU - Pass, Rafael
N1 - Publisher Copyright:
© Noam Mazor and Rafael Pass.
PY - 2024/7
Y1 - 2024/7
N2 - We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size Problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions. In more detail: Assuming the existence of indistinguishability obfuscation, and subexponentially-secure one-way functions, an appropriate Gap version of MCSP is not NP-complete under randomized Levin-reductions. Assuming the existence of subexponentially-secure indistinguishability obfuscation, subexponentially-secure one-way functions and injective PRGs, an appropriate Gap version of MKTP is not NP-complete under randomized Levin-reductions.
AB - We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size Problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions. In more detail: Assuming the existence of indistinguishability obfuscation, and subexponentially-secure one-way functions, an appropriate Gap version of MCSP is not NP-complete under randomized Levin-reductions. Assuming the existence of subexponentially-secure indistinguishability obfuscation, subexponentially-secure one-way functions and injective PRGs, an appropriate Gap version of MKTP is not NP-complete under randomized Levin-reductions.
KW - Kolmogorov complexity
KW - Levin Reduction
KW - MCSP
UR - http://www.scopus.com/inward/record.url?scp=85199357509&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.CCC.2024.36
DO - 10.4230/LIPIcs.CCC.2024.36
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AN - SCOPUS:85199357509
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 39th Computational Complexity Conference, CCC 2024
A2 - Santhanam, Rahul
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 39th Computational Complexity Conference, CCC 2024
Y2 - 22 July 2024 through 25 July 2024
ER -