The Critical Exponent is Computable for Automatic Sequences
The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. This generalizes or recovers previous results of...
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2011-08-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Summary: | The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. This generalizes or recovers previous results of Krieger and others. Our technique is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence. |
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| ISSN: | 2075-2180 |