Paper Info
Title
Inside the Binary Reflected Gray Code - Flip-Swap Languages in 2-Gray Code Order.
Abstract
A flip-swap language is a set S of binary strings of length n such that $S \cup 0^n$ is closed under two operations (when applicable): (1) Flip the leftmost 1; and (2) Swap the leftmost 1 with the bit to its right. Flip-swap languages model many combinatorial objects including necklaces, Lyndon words, prefix normal words, left factors of k-ary Dyck words, and feasible solutions to 0-1 knapsack problems. We prove that any flip-swap language forms a cyclic 2-Gray code when listed in binary reflected Gray code (BRGC) order. Furthermore, a generic successor rule computes the next string when provided with a membership tester. The rule generates each string in the aforementioned flip-swap languages in O(n)-amortized per string, except for prefix normal words of length n which require O($n^{1.864}$)-amortized per string. Our work generalizes results on necklaces and Lyndon words by Vajnovski [Inf. Process. Lett. 106(3):96$-$99, 2008].
Year
DOI
Venue
2021
10.1007/978-3-030-85088-3_15
WORDS
DocType
Citations 
PageRank 
Conference
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Joe Sawada1669.11
Aaron Williams213920.42
Dennis Wong301.01