A variant of Hofstadter's sequence and finite automata
J.-P. Allouche, J. Shallit
TL;DR
This paper investigates a variant of Hofstadter's Q-sequence, demonstrating it is 2-automatic and providing an explicit automaton for its computation.
Contribution
It introduces a new variant of Hofstadter's Q-sequence and proves its 2-automaticity with an explicit automaton, extending previous work.
Findings
The sequence is proven to be 2-automatic.
An explicit automaton computing the sequence is provided.
The work builds on and extends prior analysis of Hofstadter's sequences.
Abstract
Following up on a paper of Balamohan, Kuznetsov, and Tanny, we analyze a variant of Hofstadter's Q-sequence and show it is 2-automatic. An automaton computing the sequence is explicitly given.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Algorithms and Data Compression