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- W2095226356 abstract "The exact complexity of the weak pigeonhole principle is an old and fundamental problem in proof complexity. Using a diagonalization argument, J. B. Paris et al. (J. Symbolic Logic 53 (1988), 1235-1244) showed how to prove the weak pigeonhole principle with bounded-depth, quasipolynomialsize proofs. Their argument was further refined by J. Krajicek (J. Symbolic Logic 59 (1994), 73-86). In this paper, we present a new proof: we show that the weak pigeonhole principle has quasipolynomial-size LK proofs where every formula consists of a single AND/OR of polylog fan-in. Our proof is conceptually simpler than previous arguments, and is optimal with respect to depth." @default.
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- W2095226356 date "2000-05-01" @default.
- W2095226356 modified "2023-09-25" @default.
- W2095226356 title "A new proof of the weak pigeonhole principle" @default.
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- W2095226356 doi "https://doi.org/10.1145/335305.335348" @default.
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