{"id":{"repo_id":"duquesne","oai_identifier":"oai:dsc.duq.edu:etd-1650"},"canonical_url":"https://search.dev.ndltd.org/etd/duquesne/oai:dsc.duq.edu:etd-1650","repository":{"repo_id":"duquesne","name":"Duquesne","base_url":"https://dsc.duq.edu/do/oai/"},"display":{"title":"An Analysis of DNF Maximum Entropy","abstract":"This study focuses on the entropy of functions computed by monotone DNF formulas. Entropy, which is a measure of uncertainty, information, and choice, has been long studied in the field of mathematics and computer science. We will be considering spectral entropy and focus on the conjecture that for each fixed number of terms t, the maximum entropy of a function computed by a t-term DNF is achieved by a function computable by a read-once DNF. A Python program was written to first express the t-term DNF Boolean functions as multilinear polynomials and then to compute their spectral entropy. This was done for the cases t = 1, 2, 3, 4. Our results agree with the conjecture and show that the maximum entropy occurs for functions with a small number of literals.","abstract_html":"This study focuses on the entropy of functions computed by monotone DNF formulas. Entropy, which is a measure of uncertainty, information, and choice, has been long studied in the field of mathematics and computer science. We will be considering spectral entropy and focus on the conjecture that for each fixed number of terms t, the maximum entropy of a function computed by a t-term DNF is achieved by a function computable by a read-once DNF. A Python program was written to first express the t-term DNF Boolean functions as multilinear polynomials and then to compute their spectral entropy. This was done for the cases t = 1, 2, 3, 4. Our results agree with the conjecture and show that the maximum entropy occurs for functions with a small number of literals.","abstract_has_math":false,"creators":["Hasanaj, Belinda"],"institution":null,"degree_name":"MS","degree_level":"Immediate Access","degree_discipline":"Computational Mathematics","degree_department":null,"school":null,"contributors":["Karl Wimmer","Jeffrey Jackson","Abhay Gaur"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:09:46Z","subjects":["Boolean function","DNF formula","spectral entropy"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dsc.duq.edu/etd/634","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Karl Wimmer","Jeffrey Jackson","Abhay Gaur"]},{"key":"dc:creator","label":"Author","values":["Hasanaj, Belinda"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-08-03T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computational Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Immediate Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Boolean function","DNF formula","spectral entropy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dsc.duq.edu/etd/634"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This study focuses on the entropy of functions computed by monotone DNF formulas. Entropy, which is a measure of uncertainty, information, and choice, has been long studied in the field of mathematics and computer science. We will be considering spectral entropy and focus on the conjecture that for each fixed number of terms t, the maximum entropy of a function computed by a t-term DNF is achieved by a function computable by a read-once DNF. A Python program was written to first express the t-term DNF Boolean functions as multilinear polynomials and then to compute their spectral entropy. This was done for the cases t = 1, 2, 3, 4. Our results agree with the conjecture and show that the maximum entropy occurs for functions with a small number of literals."]},{"key":"dc:title","label":"Title","values":["An Analysis of DNF Maximum Entropy"]}]}],"canonical_facts":{"dc:contributor":["Karl Wimmer","Jeffrey Jackson","Abhay Gaur"],"dc:creator":["Hasanaj, Belinda"],"dc:date.available":["2018-08-03T07:00:00Z"],"dc:description.abstract":["This study focuses on the entropy of functions computed by monotone DNF formulas. Entropy, which is a measure of uncertainty, information, and choice, has been long studied in the field of mathematics and computer science. We will be considering spectral entropy and focus on the conjecture that for each fixed number of terms t, the maximum entropy of a function computed by a t-term DNF is achieved by a function computable by a read-once DNF. A Python program was written to first express the t-term DNF Boolean functions as multilinear polynomials and then to compute their spectral entropy. This was done for the cases t = 1, 2, 3, 4. Our results agree with the conjecture and show that the maximum entropy occurs for functions with a small number of literals."],"dc:identifier":["https://dsc.duq.edu/etd/634"],"dc:language":["English"],"dc:subject":["Boolean function","DNF formula","spectral entropy"],"dc:title":["An Analysis of DNF Maximum Entropy"],"thesis:degree_discipline":["Computational Mathematics"],"thesis:degree_level":["Immediate Access"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T02:09:46Z"}