
A Separation of γ and b via Thue–Morse Words
We prove that for n≥ 2, the size b(t_n) of the smallest bidirectional sc...
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Arbitrarylength analogs to de Bruijn sequences
Let α be a lengthL cyclic sequence of characters from a sizeK alphabet...
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StringtoString Interpretations with PolynomialSize Output
Stringtostring MSO interpretations are like Courcelle's MSO transducti...
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Stochastic Lsystem Inference from Multiple String Sequence Inputs
Lindenmayer systems (Lsystems) are a grammar system that consist of str...
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Smoothed Analysis of Trie Height by Starlike PFAs
Tries are general purpose data structures for information retrieval. The...
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Sensitivity of string compressors and repetitiveness measures
The sensitivity of a string compression algorithm C asks how much the ou...
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On Stricter Reachable Repetitiveness Measures*
The size b of the smallest bidirectional macro scheme, which is arguably...
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String Attractors for Automatic Sequences
We show that it is decidable, given an automatic sequence s and a constant c, whether all prefixes of s have a string attractor of size ≤ c. Using a decision procedure based on this result, we show that all prefixes of the perioddoubling sequence of length ≥ 2 have a string attractor of size 2. We also prove analogous results for other sequences, including the ThueMorse sequence and the Tribonacci sequence. We also provide general upper and lower bounds on string attractor size for different kinds of sequences. For example, if s has a finite appearance constant, then there is a string attractor for s[0..n1] of size O(log n). If further s is linearly recurrent, then there is a string attractor for s[0..n1] of size O(1). For automatic sequences, the size of the smallest string attractor for s[0..n1] is either Θ(1) or Θ(log n), and it is decidable which case occurs. Finally, we close with some remarks about greedy string attractors.
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