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- W4307652577 abstract "The minimum number of clauses in a CNF representation of the parity function $x_1 oplus x_2 oplus dotsb oplus x_n$ is $2^{n-1}$. One can obtain a more compact CNF encoding by using non-deterministic variables (also known as guess or auxiliary variables). In this paper, we prove the following lower bounds, that almost match known upper bounds, on the number $m$ of clauses and the maximum width $k$ of clauses: 1) if there are at most $s$ auxiliary variables, then $m ge Omegaleft(2^{n/(s+1)}/nright)$ and $k ge n/(s+1)$; 2) the minimum number of clauses is at least $3n$. We derive the first two bounds from the Satisfiability Coding Lemma due to Paturi, Pudlak, and Zane." @default.
- W4307652577 created "2022-11-04" @default.
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- W4307652577 date "2022-03-02" @default.
- W4307652577 modified "2023-09-26" @default.
- W4307652577 title "CNF Encodings of Parity" @default.
- W4307652577 doi "https://doi.org/10.48550/arxiv.2203.01082" @default.
- W4307652577 hasPublicationYear "2022" @default.
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