Partition and Test (Apply Divide and Conquer rule)

For testing of digital vlsi circuits you can use Design for testability tools . it includes BIST-Built in self Test, ATPG-automatic Test pattern generation,Scan Chains etc..

http://nptel.ac.in/courses/106103116/

http://www.learnerstv.com/Free-Computer-Science-Video-lectures-ltv834-Page1.htm

http://ieeexplore.ieee.org/document/522700/

Essentials of Electronic Testing for Digital, Memory and Mixed-Signal VLSI

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http://soc.cs.nchu.edu.tw/pllai/NCUT/vlsi100-2/Chapter%201%20Introduction%20to%20VLSI%20Testing.pdf