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This keynote lecture explores the approaches to implement intelligent behaviors by biological organisms, silicon automata, and computing systems. Autonomous computing is introduced as the latest and advanced computing techniques built upon routine, algorithmic, and adaptive systems. The theory and philosophy behind autonomous computing is cognitive informatics. In other words, autonomous computing systems are applications of cognitive informatics. A Layered Reference Model of the Brain (LRMB) and its cognitive mechanisms and processes are described in this talk, which form the foundation for designing and implementing autonomous computing systems. Real-Time Process Algebra (RTPA) is introduced to formally and rigorously describe autonomous computing systems and cognitive behaviors. It is believed that applications of cognitive informatics and autonomous computing will result in the development of new generation computing architectures and novel information processing systems.