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- W4300877209 abstract "We consider the problem of efficiently enumerating the satisfying assignments to $AC^0$ circuits. We give a zero-error randomized algorithm which takes an $AC^0$ circuit as input and constructs a set of restrictions which partition ${0,1}^n$ so that under each restriction the value of the circuit is constant. Let $d$ denote the depth of the circuit and $cn$ denote the number of gates. This algorithm runs in time $|C| 2^{n(1-mu_{c.d})}$ where $|C|$ is the size of the circuit for $mu_{c,d} ge 1/bigO[lg c + d lg d]^{d-1}$ with probability at least $1-2^{-n}$. As a result, we get improved exponential time algorithms for $AC^0$ circuit satisfiability and for counting solutions. In addition, we get an improved bound on the correlation of $AC^0$ circuits with parity. As an important component of our analysis, we extend the H{aa}stad Switching Lemma to handle multiple $kcnf$s and $kdnf$s." @default.
- W4300877209 created "2022-10-04" @default.
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- W4300877209 date "2011-07-15" @default.
- W4300877209 modified "2023-09-27" @default.
- W4300877209 title "A Satisfiability Algorithm for AC$^0$" @default.
- W4300877209 doi "https://doi.org/10.48550/arxiv.1107.3127" @default.
- W4300877209 hasPublicationYear "2011" @default.
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