Browsing Theses by Subject "automatic sequences"
Now showing items 1-5 of 5
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Automatic Sequences and Decidable Properties: Implementation and Applications
(University of Waterloo, 2013-09-19)In 1912 Axel Thue sparked the study of combinatorics on words when he showed that the Thue-Morse sequence contains no overlaps, that is, factors of the form ayaya. Since then many interesting properties of sequences began ... -
Deciding Properties of Automatic Sequences
(University of Waterloo, 2013-09-24)In this thesis, we show that several natural questions about automatic sequences can be expressed as logical predicates and then decided mechanically. We extend known results in this area to broader classes of sequences ... -
Decision Algorithms for Ostrowski-Automatic Sequences
(University of Waterloo, 2020-05-13)We extend the notion of automatic sequences to a broader class, the Ostrowski-automatic sequences. We develop a procedure for computationally deciding certain combinatorial and enumeration questions about such sequences ... -
Sparse Automatic Sets
(University of Waterloo, 2020-11-26)The theory of automatic sets and sequences arises naturally in many different areas of mathematics, notably in the study of algebraic power series in positive characteristic, due to work of Christol, and in Derksen's ... -
Variations on the Erdos Discrepancy Problem
(University of Waterloo, 2012-01-04)The Erdős discrepancy problem asks, "Does there exist a sequence t = {t_i}_{1≤i<∞} with each t_i ∈ {-1,1} and a constant c such that |∑_{1≤i≤n} t_{id}| ≤ c for all n,c ∈ ℕ = {1,2,3,...}?" The discrepancy of t equals ...