{'fraction_non_alphanumeric': 0.03253012048192771, 'fraction_numerical': 0.0, 'mean_word_length': 5.295454545454546, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, '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}}
A translation of weighted LTL formulas to weighted Büchi automata over ω-valuation monoids

In this paper we introduce a weighted LTL over product {\omega}-valuation monoids that satisfy specific properties. We also introduce weighted generalized Buchi automata with {\epsilon}-transitions, as well as weighted Buchi automata with {\epsilon}-transitions over product {\omega}-valuation monoids and prove that these two models are expressively equivalent and also equivalent to weighted Buchi automata already introduced in the literature. We prove that every formula of a syntactic fragment of our logic can be effectively translated to a weighted generalized Buchi automaton with {\epsilon}-transitions. Finally, we prove that the number of states of the produced automaton is polynomial in the size of the corresponding formula.