Automata on Terms
The theory of finite automata has many interesting and useful generalizations that allow more general types of inputs, such as infinite strings and finite and infinite trees In this lecture and the next we will study one such generalization: finite automata on terms, also known as finite labeled trees. This generalization is quite natural and has a decidedly algebraical ebraic flavor. In particular, we will show that the entire Myhill—Nerode theory developed in Lectures 13 through 16 is really a consequence of basic results in universal algebra, a branch of algebra that deals with general algebraic concepts such as direct product, homomorphism, homomorphic image, and quotient algebra.
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