{"id":{"repo_id":"duquesne","oai_identifier":"oai:dsc.duq.edu:etd-1409"},"canonical_url":"https://search.dev.ndltd.org/etd/duquesne/oai:dsc.duq.edu:etd-1409","repository":{"repo_id":"duquesne","name":"Duquesne","base_url":"https://dsc.duq.edu/do/oai/"},"display":{"title":"Towards Optimal Tree Construction of Monotone Functions","abstract":"This thesis focuses on finding counterexamples for the conjecture suggested by Dr. Jackson that if two Boolean variables i and j in a monotone Boolean function have the relation such that if i is relevant in only one sub-tree with j as root while j is relevant in both sub-trees with i as root, then the optimal tree size (defined as the number of leaves in the tree) with j as root is as least as small as the optimal tree size with i as root. All distinct monotone Boolean functions of up to 6 variables and some interesting functions of 7 and 8 variables are tested; no counterexample has been found.","abstract_html":"This thesis focuses on finding counterexamples for the conjecture suggested by Dr. Jackson that if two Boolean variables i and j in a monotone Boolean function have the relation such that if i is relevant in only one sub-tree with j as root while j is relevant in both sub-trees with i as root, then the optimal tree size (defined as the number of leaves in the tree) with j as root is as least as small as the optimal tree size with i as root. All distinct monotone Boolean functions of up to 6 variables and some interesting functions of 7 and 8 variables are tested; no counterexample has been found.","abstract_has_math":false,"creators":["Chen, Miao"],"institution":null,"degree_name":"MS","degree_level":"Immediate Access","degree_discipline":"Computational Mathematics","degree_department":null,"school":null,"contributors":["Jeffrey Jackson","Donald L. Simon","Patrick Juola"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-01-01T08:00:00Z","date_published":"2005-01-01T08:00:00Z","updated_at":"2026-07-24T02:09:27Z","subjects":["disjunctive normal form","influence","monotone Boolean decision tree","monotone Boolean function","optimal tree construction","optimal tree size"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dsc.duq.edu/etd/396","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jeffrey Jackson","Donald L. 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All distinct monotone Boolean functions of up to 6 variables and some interesting functions of 7 and 8 variables are tested; no counterexample has been found."]},{"key":"dc:title","label":"Title","values":["Towards Optimal Tree Construction of Monotone Functions"]}]}],"canonical_facts":{"dc:contributor":["Jeffrey Jackson","Donald L. Simon","Patrick Juola"],"dc:creator":["Chen, Miao"],"dc:date.available":["2018-08-03T07:00:00Z"],"dc:description.abstract":["This thesis focuses on finding counterexamples for the conjecture suggested by Dr. Jackson that if two Boolean variables i and j in a monotone Boolean function have the relation such that if i is relevant in only one sub-tree with j as root while j is relevant in both sub-trees with i as root, then the optimal tree size (defined as the number of leaves in the tree) with j as root is as least as small as the optimal tree size with i as root. All distinct monotone Boolean functions of up to 6 variables and some interesting functions of 7 and 8 variables are tested; no counterexample has been found."],"dc:identifier":["https://dsc.duq.edu/etd/396"],"dc:language":["English"],"dc:subject":["disjunctive normal form","influence","monotone Boolean decision tree","monotone Boolean function","optimal tree construction","optimal tree size"],"dc:title":["Towards Optimal Tree Construction of Monotone Functions"],"thesis:degree_discipline":["Computational Mathematics"],"thesis:degree_level":["Immediate Access"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T02:09:27Z"}