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Magic Numbers in Periodic Sequences

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Combinatorics on Words (WORDS 2023)

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 a minimal 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.

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Notes

  1. 1.

    Proofs omitted due to space constraints may be found at https://arxiv.org/abs/2304.03268.

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Acknowledgments

Savinien Kreczman and Manon Stipulanti are supported by the FNRS Research grants 1.A.789.23F and 1.B.397.20F respectively.

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Correspondence to Manon Stipulanti .

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Kreczman, S., Prigioniero, L., Rowland, E., Stipulanti, M. (2023). Magic Numbers in Periodic Sequences. In: Frid, A., Mercaş, R. (eds) Combinatorics on Words. WORDS 2023. Lecture Notes in Computer Science, vol 13899. Springer, Cham. https://doi.org/10.1007/978-3-031-33180-0_16

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  • DOI: https://doi.org/10.1007/978-3-031-33180-0_16

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