## Notre Dame Journal of Formal Logic

### Simplified Lower Bounds for Propositional Proofs

#### Abstract

This article presents a simplified proof of the result that bounded depth propositional proofs of the pigeonhole principle are exponentially large. The proof uses the new techniques for proving switching lemmas developed by Razborov and Beame. A similar result is also proved for some examples based on graphs.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 37, Number 4 (1996), 523-544.

Dates
First available in Project Euclid: 16 December 2002

https://projecteuclid.org/euclid.ndjfl/1040046140

Digital Object Identifier
doi:10.1305/ndjfl/1040046140

Mathematical Reviews number (MathSciNet)
MR1446227

Zentralblatt MATH identifier
0882.03052

Subjects
Primary: 03F20: Complexity of proofs

#### Citation

Urquhart, Alasdair; Fu, Xudong. Simplified Lower Bounds for Propositional Proofs. Notre Dame J. Formal Logic 37 (1996), no. 4, 523--544. doi:10.1305/ndjfl/1040046140. https://projecteuclid.org/euclid.ndjfl/1040046140

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