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This paper will introduce the theory and practice of DNA-based computing models (DNAbCM). Several models will be provided with the basic tools necessary to understand current research in DNAbCM. Discussion will focus on potential applications to artificial intelligence, scheduling problem, molecular memory and smart machines (or bio-robotics). Following a brief review of DNA structure, an overview of the basic tools from molecular biology utilized in biotechnology (e.g., DNA molecular annealing, ligation, polymerization, restriction enzyme, PCR and POA etc.) will be undertaken. A discussion of the major, basic computational architectures of classical DNA computing models (e.g., Adleman's algorithm for HPP, DNA Chip-based SAT, and etc.) will be provided in each presenting an animation detailing execution of a simple example. Attention will then turn to advanced topics related to molecular memory, hybrid artificial intelligence, in particular, a new semantic network and scheduling smart machine will be presented and implemented on a DNAbCM-inspired semantic model. This discussion on the models and implementations will be undertaken with attention to both theoretical and chemical points of view.