1. 1 Resolution loss Error-correcting schemes mentioned above always generates a resolution loss. Compact proofreading [Sahu, Reif, Yin ’04] is proposed to remove the resolution loss. However, [Soloveichik, Winfree ’05] showed that compact proofreading requires increasing number of tiles exponentially. We propose “dimension augmentation” technique to solve this problem.

2. 2 Dimension Augmentation k The original systemOdd and even duplicatesk duplicates on the third dimension E EE E EE E EE E EE E EE E EE O OO O OO O OO O OO O OO O OO

3. 3 Dimension Augmentation No resolution loss in the original two dimensions. Increase the number of tiles linearly. Provably correct for an example tile system called “parity system” Correctness in general remains open.

4. 4 Parity System

5. 5 Barish, Rothermund, Winfree, 2005