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In the past decade, explosive growth in computer networks has brought security issues to the forefront. One of the greatest challenges in computer security today is the software assurance problem: How do we deal with the fact that our most trusted software, even our security software itself, is often buggy? In this talk, I will discuss how static analysis can help with the software assurance problem. I will describe some recent experience with static analysis tools for vulnerability detection. I will also survey a number of open problems in the field and suggest a few promising directions for future research.