Closed, Palindromic, Rich, Privileged, Trapezoidal, and Balanced Words in Automatic Sequences

[摘要] We prove that the property of being closed (resp., palindromic, rich, privileged trapezoidal, balanced) is expressible in first-order logic for automatic (and some related) sequences. It therefore follows that the characteristic function of those $n$ for

[学科分类] 离散数学和组合数学

[关键词] Decision procedure;Closed word;Palindrome;Rich word;Privileged word;Trapezoidal word;Balanced word;Thue-Morse sequence;Rudin-Shapiro sequence