{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86941"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86941","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Count and Tree in Uniform NC(1)","abstract":"Based on the function algebras of $AC\\sp0$ and $NC\\sp1$ (in (9)), we prove the following results: (1) count is in uniform $NC\\sp1.$ (2) The equivalence of tree and k-BRN. (3) Multiple addition is in uniform $TC\\sp0.$ (4) tree is uniform $NC\\sp1$ complete under $AC\\sp0$ reduction. We also discuss weak multiple product which is computable in uniform $TC\\sp0.$ All proofs here are function algebraic.","abstract_html":"Based on the function algebras of $AC\\sp0$ and $NC\\sp1$ (in (9)), we prove the following results: (1) count is in uniform $NC\\sp1.$ (2) The equivalence of tree and k-BRN. (3) Multiple addition is in uniform $TC\\sp0.$ (4) tree is uniform $NC\\sp1$ complete under $AC\\sp0$ reduction. We also discuss weak multiple product which is computable in uniform $TC\\sp0.$ All proofs here are function algebraic.","abstract_has_math":true,"creators":["Lee, Jui-Lin"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Takeuti, Gaisi"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:16Z","date_published":"2015-09-28T15:20:16Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Computer Science"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9717298"],"render_values":[{"text":"(MiAaPQ)AAI9717298","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86941","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Takeuti, Gaisi"]},{"key":"dc:creator","label":"Author","values":["Lee, Jui-Lin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:16Z","10000-01-01","1997"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86941","(MiAaPQ)AAI9717298"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Based on the function algebras of $AC\\sp0$ and $NC\\sp1$ (in (9)), we prove the following results: (1) count is in uniform $NC\\sp1.$ (2) The equivalence of tree and k-BRN. (3) Multiple addition is in uniform $TC\\sp0.$ (4) tree is uniform $NC\\sp1$ complete under $AC\\sp0$ reduction. We also discuss weak multiple product which is computable in uniform $TC\\sp0.$ All proofs here are function algebraic.","Made available in DSpace on 2015-09-28T15:20:16Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9717298.pdf: 3634121 bytes, checksum: 7de0f14c3ae94cc597547a661161d5d5 (MD5) Previous issue date: 1997","Embargo set by: Seth Robbins for item 88222 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","87 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997."]},{"key":"dc:title","label":"Title","values":["Count and Tree in Uniform NC(1)"]}]}],"canonical_facts":{"dc:contributor":["Takeuti, Gaisi"],"dc:creator":["Lee, Jui-Lin"],"dc:date":["2015-09-28T15:20:16Z","10000-01-01","1997"],"dc:description":["Based on the function algebras of $AC\\sp0$ and $NC\\sp1$ (in (9)), we prove the following results: (1) count is in uniform $NC\\sp1.$ (2) The equivalence of tree and k-BRN. (3) Multiple addition is in uniform $TC\\sp0.$ (4) tree is uniform $NC\\sp1$ complete under $AC\\sp0$ reduction. We also discuss weak multiple product which is computable in uniform $TC\\sp0.$ All proofs here are function algebraic.","Made available in DSpace on 2015-09-28T15:20:16Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9717298.pdf: 3634121 bytes, checksum: 7de0f14c3ae94cc597547a661161d5d5 (MD5) Previous issue date: 1997","Embargo set by: Seth Robbins for item 88222 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","87 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997."],"dc:identifier":["http://hdl.handle.net/2142/86941","(MiAaPQ)AAI9717298"],"dc:language":["eng"],"dc:subject":["Computer Science"],"dc:title":["Count and Tree in Uniform NC(1)"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}