Size Complexity of Two-Way Finite Automata

This is a talk on the size complexity of two-way finite automata. We present the central open problem in the area, explain a motivation behind it, recall its early history, and introduce some of the concepts used in its study. We then sketch a possible future, describe a natural systematic way of pursuing it, and record some of the progress that has been achieved. We add little to what is already known--only exposition, terminology, and questions.

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