Abstract
We introduce the notion of a regular language, and show that regular languages are precisely those that are accepted by deterministic finite automata. We introduce nondeterminism, and prove that for automata, nondeterministic and deterministic machines have the same power, the trade-off being an exponential increase in the number of states. We finish with the Myhill-Nerode Theorem which shows how finite state is that same as having finite index for a certain canonical equivalence relation.
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© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
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Downey, R. (2024). Regular Languages and Finite Automata. In: Computability and Complexity. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-53744-8_2
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DOI: https://doi.org/10.1007/978-3-031-53744-8_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-031-53743-1
Online ISBN: 978-3-031-53744-8
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