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cs.FL2023★ 2 cited
A General Approach to Proving Properties of Fibonacci Representations via Automata Theory
Jeffrey Shallit, Sonja Linghui Shan
We provide a method, based on automata theory, to mechanically prove the correctness of many numeration systems based on Fibonacci numbers. With it, long case-based and induction-b…
cs.FL2022
Automatic Sequences in Negative Bases and Proofs of Some Conjectures of Shevelev
Jeffrey Shallit, Sonja Linghui Shan, Kai Hsiang Yang
We discuss the use of negative bases in automatic sequences. Recently the theorem-prover Walnut has been extended to allow the use of base (-k) to express variables, thus permittin…