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Electronic Colloquium on Computational Complexity

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Reports tagged with algorithmic method:
TR22-048 | 4th April 2022
Hanlin Ren, Rahul Santhanam, Zhikun Wang

On the Range Avoidance Problem for Circuits

We consider the range avoidance problem (called Avoid): given the description of a circuit $C:\{0, 1\}^n \to \{0, 1\}^\ell$ (where $\ell > n$), find a string $y\in\{0, 1\}^\ell$ that is not in the range of $C$. This problem is complete for the class APEPP that corresponds to explicit constructions of ... more >>>

TR22-183 | 19th December 2022
Lijie Chen

New Lower Bounds and Derandomization for ACC, and a Derandomization-centric View on the Algorithmic Method

In this paper, we obtain several new results on lower bounds and derandomization for ACC^0 circuits (constant-depth circuits consisting of AND/OR/MOD_m gates for a fixed constant m, a frontier class in circuit complexity):

1. We prove that any polynomial-time Merlin-Arthur proof system with an ACC^0 verifier (denoted by ... more >>>

TR23-072 | 18th May 2023
Yeyuan Chen, Yizhi Huang, Jiatu Li, Hanlin Ren

Range Avoidance, Remote Point, and Hard Partial Truth Tables via Satisfying-Pairs Algorithms

The *range avoidance problem*, denoted as $\mathcal{C}$-$\rm Avoid$, asks to find a non-output of a given $\mathcal{C}$-circuit $C:\{0,1\}^n\to\{0,1\}^\ell$ with stretch $\ell>n$. This problem has recently received much attention in complexity theory for its connections with circuit lower bounds and other explicit construction problems. Inspired by the Algorithmic Method for circuit ... more >>>

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