{'fraction_non_alphanumeric': 0.009746588693957114, 'fraction_numerical': 0.0, 'mean_word_length': 5.8533333333333335, '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}}
Spectral theory of disjunctive decomposition for balanced Boolean functions

A theory has been developed to identify simple disjunctive decomposition of balanced Boolean functions through the Walsh spectrum of such functions. Many common logic circuits such as adders, parity checkers and multiplexers are balanced Boolean functions. Here, various types of decomposition of the balanced functions are considered and their corresponding spectral conditions that have to be satisfied for their existence are listed.