{'fraction_non_alphanumeric': 0.017721518987341773, 'fraction_numerical': 0.0, 'mean_word_length': 5.387096774193548, '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}}
Counting in trees

We consider automata and logics that allow to reason about numerical properties of unranked trees, expressed as Presburger constraints. We characterize non-deterministic automata by Presburger Monadic Second-Order logic, and deterministic automata by Presburger Fixpoint logic. We show how our results can be used in order to obtain efficient querying algorithms on XML trees.