Magic numbers in periodic sequences
Abstract
In formal languages and automata theory, the magic number problem can be formulated as follows: for a given integer n, is it possible to find a number d in the range [n,2^n] such that there is no minimal deterministic finite automaton with d states that can be simulated by an optimal nondeterministic finite automaton with exactly n states? If such a number d exists, it is called magic. In this paper, we consider the magic number problem in the framework of deterministic automata with output, which are known to characterize automatic sequences. More precisely, we investigate magic numbers for periodic sequences viewed as either automatic, regular, or constant-recursive.
Keywords
Cite
@article{arxiv.2304.03268,
title = {Magic numbers in periodic sequences},
author = {Savinien Kreczman and Luca Prigioniero and Eric Rowland and Manon Stipulanti},
journal= {arXiv preprint arXiv:2304.03268},
year = {2023}
}
Comments
19 pages, 2 figures, 3 tables, accepted at the international conferences WORDS 2023