Abstract
In Section 4.4, we defined generalized derivatives. This chapter attempts to take derivatives as far as we can. In particular, we define them for the most general expressions considered in this book, namely expressions with union, concatenation, star, and complementation. We formulate the corresponding version of the λ-property and derive several useful properties of these derivatives. Most significantly, it allows us to show that any explicit equation has a unique solution, provided its expression has this λ-property. We conclude the chapter with a discussion of techniques that permit us to determine whether a given word is in the solution, even though that solution may not be regular.
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© 1999 Springer Science+Business Media New York
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Leiss, E.L. (1999). More on Generalized Derivatives. In: Language Equations. Monographs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2156-2_5
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DOI: https://doi.org/10.1007/978-1-4612-2156-2_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7436-0
Online ISBN: 978-1-4612-2156-2
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