Complexity of Linear Subsequences of $k$-Automatic Sequences

Delaram Moradi; Narad Rampersad; Jeffrey Shallit

Paper

Complexity of Linear Subsequences of $k$-Automatic Sequences

Abstract

We construct automata with input(s) in base

recognizing some basic relations and study their number of states. We also consider some basic operations on

-automatic sequences and discuss their state complexity. We find a relationship between subword complexity of the interior sequence

and state complexity of the linear subsequence

. We resolve a recent question of Zantema and Bosma about linear subsequences of

-automatic sequences with input in most-significant-digit-first format. We also discuss the state complexity and runtime complexity of using a reasonable interpretation of Büchi arithmetic to actually construct some of the studied automata recognizing relations or carrying out operations on automatic sequences.