{'fraction_non_alphanumeric': 0.03669724770642202, 'fraction_numerical': 0.011009174311926606, 'mean_word_length': 4.571428571428571, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On the growth rates of complexity of threshold languages

Threshold languages, which are the (k/k-1)) + -free languages over k-letter alphabets with k > 5, are the minimal infinite power-free languages according to Dejean's conjecture, which is now proved for all alphabets. We study the growth properties of these languages. On the base of obtained structural properties and computer-assisted studies we conjecture that the growth rate of complexity of the threshold language over k letters tends to a constant α ≈ 1.242 as k tends to infinity.