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Automatic Sequences - Theory, Applications, Generalizations
TLDR
This chapter discusses automata, automatic sequences, and other models of computation in number theory and algebra, as well as number systems and numeration systems, and some examples of these models are presented.
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The Ring of k-Regular Sequences
TLDR
The automatic sequence is the central concept at the intersection of formal language theory and number theory, and has been extensively studied by Christol, Kamae, Mendes France and Rauzy, and other writers.
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Automatic Sequences: Frequency of Letters
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The ring of k-regular sequences, II
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The Ubiquitous Prouhet-Thue-Morse Sequence
TLDR
The Prouhet-Thue-Morse sequence appears to be somewhat ubiquitous, and it is described many of its apparently unrelated occurrences.
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Automatic Sequences: Cobham's Theorem
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A Second Course in Formal Languages and Automata Theory
TLDR
Many topics often absent from other textbooks, such as repetitions in words, state complexity, the interchange lemma, 2DPDAs, and the incompressibility method are covered here.
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Regular Expressions: New Results and Open Problems
TLDR
Regular expressions have been studied for nearly 50 years, yet many intriguing problems about their descriptive capabilities remain open and some new results are sketches.
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Algorithmic Number Theory
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A Lower Bound Technique for the Size of Nondeterministic Finite Automata
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