15 citations · 105 across the 66 of their papers we have counts for
5 papers · 1 filter
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…
Proving properties of some greedily-defined integer recurrences via automata theory
Jeffrey Shallit
Venkatachala on the one hand, and Avdispahić & Zejnulahi on the other, both studiied integer sequences with an unusual sum property defined in a greedy way, and proved many results…
Proving Properties of -Representations with the Walnut Theorem-Prover
Jeffrey Shallit
We revisit a classic theorem of Frougny and Sakarovitch concerning automata for -representations, and show how to obtain it in a different and more computationally direct way. U…
Transduction of Automatic Sequences and Applications
Jeffrey Shallit, Anatoly Zavyalov
We consider the implementation of the transduction of automatic sequences, and their generalizations, in the Walnut software for solving decision problems in combinatorics on words…
Rudin-Shapiro Sums Via Automata Theory and Logic
Narad Rampersad, Jeffrey Shallit
We show how to obtain, via a unified framework provided by logic and automata theory, many classical results of Brillhart and Morton on Rudin-Shapiro sums. The techniques also faci…