Improved lower bounds of tilde-Omega(n to the 2/3) queries for one-sided testers and Omega(sqrt(n)) for two-sided testers of directed acyclicity in the unidirectional bounded out-degree model, plus Omega(n) for tolerant testing via reduction from 3-colorability.
Goldreich.Introduction to Property Testing
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Lower Bounds for Testing Directed Acyclicity in the Unidirectional Bounded-Degree Model
Improved lower bounds of tilde-Omega(n to the 2/3) queries for one-sided testers and Omega(sqrt(n)) for two-sided testers of directed acyclicity in the unidirectional bounded out-degree model, plus Omega(n) for tolerant testing via reduction from 3-colorability.