The Minimum Oracle Circuit Size Problem

Limits of Minimum Circuit Size Problem as Oracle

The Minimum Circuit Size Problem (MCSP) is known to be hard for statistical zero knowledge via a BPP-reduction (Allender and Das, 2014), whereas establishing NP-hardness of MCSP via a polynomial-time many-one reduction is difficult (Murray and Williams, 2015) in the sense that it implies ZPP 6= EXP, which is a major open problem in computational complexity. In this paper, we provide strong evid...

On the NP-Completeness of the Minimum Circuit Size Problem

We study the Minimum Circuit Size Problem (MCSP): given the truth-table of a Boolean function f and a number k, does there exist a Boolean circuit of size at most k computing f? This is a fundamental NP problem that is not known to be NP-complete. Previous work has studied consequences of the NP-completeness of MCSP. We extend this work and consider whether MCSP may be complete for NP under mor...

Discrete Logarithm and Minimum Circuit Size

This paper shows that the Discrete Logarithm Problem is in ZPP (where MCSP is the Minimum Circuit Size Problem). This result improves the previous bound that the Discrete Logarithm Problem is in BPP Allender et al. (2006). In doing so, this paper helps classify the relative difficulty of the Minimum Circuit Size Problem.

NP-hardness of Minimum Circuit Size Problem for OR-AND-MOD Circuits

The Minimum Circuit Size Problem (MCSP) asks for the size of the smallest boolean circuit that computes a given truth table. It is a prominent problem in NP that is believed to be hard, but for which no proof of NP-hardness has been found. A significant number of works have demonstrated the central role of this problem and its variations in diverse areas such as cryptography, derandomization, p...

The Noisy Oracle Problem