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This talk will discuss issues and methods for survivability of systems under malicious attacks. To protect from such attacks, it is necessary to take steps to prevent attacks from succeeding. At the same time, it is important to recognize that not all attacks can be averted at the outset; attacks that are successful to some degree must be recognized as unavoidable and comprehensive support for identifying and responding to attacks is required.In my talk, I will describe the recent research on attack graphs that represent known attack sequences attackers can use to penetrate computer networks. I will show how attack graphs can be used to compute actual sets of hardening measures that guarantee the safety of given critical resources. Attack graphs can also be used to correlate received alerts, hypothesize missing alerts, and predict future alerts, all at the same time. Thus, they offer a promising solution for administrators to monitor and predict the progress of an intrusion, and take appropriate countermeasures in a timely manner.