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This paper examines consciousness from the perspective of theoretical computer science (TCS), a branch of mathematics concerned with understanding the underlying principles of computation and complexity, including the implications and surprising consequences of resource limitations. We propose a formal TCS model, the Conscious Turing Machine (CTM). The CTM is influenced by Alan Turing's simple yet powerful model of computation, the Turing machine (TM), and by the global workspace theory (GWT) of consciousness originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, Jean-Pierre Changeux, George Mashour, and others. Phenomena generally associated with consciousness, such as blindsight, inattentional blindness, change blindness, dream creation, and free will, are considered. Explanations derived from the model draw confirmation from consistencies at a high level, well above the level of neurons, with the cognitive neuroscience literature.