{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19109"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19109","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The power of parallel time","abstract":"\"In this thesis, we address the following question: Are parallel machines always faster than sequential machines? Our approach is to examine the common machine models of sequential computation. For each such machine ${\\cal M}$ that runs in time T, we determine whether it is possible to speed up ${\\cal M}$ by a \"\"parallel version\"\" ${\\cal M}\\sp\\prime$ of ${\\cal M}$ that runs in time o(T). We find that the answer is affirmative for a wide range of machine models, including the tree Turing machine, the multidimensional Turing machine, the log-cost RAM (random access machine), the unit-cost RAM, and the pointer machine. All previous speedup results either relied on the severe limitation on the storage structure of ${\\cal M}$ (e.g., ${\\cal M}\\sp\\prime$ was a Turing machine with linear tapes) or required that ${\\cal M}\\sp\\prime$ had a more versatile storage structure than ${\\cal M}$ (e.g., ${\\cal M}\\sp\\prime$ was a PRAM (parallel RAM), and ${\\cal M}$ was a Turing machine with linear tapes). It was unclear whether it was the parallelism or the restriction on the storage structures (or the combination of both) that realized such speedup. We remove the above restrictions on storage structures in previous results. We present speedup theorems where the storage medium of ${\\cal M}\\sp\\prime$ is the same as (or even weaker than) that of ${\\cal M}$. Hence, parallelism alone suffices to achieve a speedup. One implication is that there does not exist any recursive function that is \"\"inherently not parallelizable.\"\"\"","abstract_html":""In this thesis, we address the following question: Are parallel machines always faster than sequential machines? Our approach is to examine the common machine models of sequential computation. For each such machine ${\\cal M}$ that runs in time T, we determine whether it is possible to speed up ${\\cal M}$ by a ""parallel version"" ${\\cal M}\\sp\\prime$ of ${\\cal M}$ that runs in time o(T). We find that the answer is affirmative for a wide range of machine models, including the tree Turing machine, the multidimensional Turing machine, the log-cost RAM (random access machine), the unit-cost RAM, and the pointer machine. All previous speedup results either relied on the severe limitation on the storage structure of ${\\cal M}$ (e.g., ${\\cal M}\\sp\\prime$ was a Turing machine with linear tapes) or required that ${\\cal M}\\sp\\prime$ had a more versatile storage structure than ${\\cal M}$ (e.g., ${\\cal M}\\sp\\prime$ was a PRAM (parallel RAM), and ${\\cal M}$ was a Turing machine with linear tapes). It was unclear whether it was the parallelism or the restriction on the storage structures (or the combination of both) that realized such speedup. We remove the above restrictions on storage structures in previous results. We present speedup theorems where the storage medium of ${\\cal M}\\sp\\prime$ is the same as (or even weaker than) that of ${\\cal M}$. Hence, parallelism alone suffices to achieve a speedup. One implication is that there does not exist any recursive function that is ""inherently not parallelizable."""","abstract_has_math":true,"creators":["Mak, Ka Ho"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Loui, Michael C."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T11:57:13Z","date_published":"2011-05-07T11:57:13Z","updated_at":"2026-07-22T22:25:12Z","subjects":["Computer Science"],"languages":["eng"],"rights":["Copyright 1995 Mak, Ka Ho"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9543665","(UMI)AAI9543665"],"render_values":[{"text":"AAI9543665","href":null,"code":true},{"text":"(UMI)AAI9543665","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19109","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Loui, Michael C."]},{"key":"dc:creator","label":"Author","values":["Mak, Ka Ho"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T11:57:13Z","10000-01-01","1995"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"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"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Mak, Ka Ho"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9543665","(UMI)AAI9543665","http://hdl.handle.net/2142/19109"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"In this thesis, we address the following question: Are parallel machines always faster than sequential machines? Our approach is to examine the common machine models of sequential computation. For each such machine ${\\cal M}$ that runs in time T, we determine whether it is possible to speed up ${\\cal M}$ by a \"\"parallel version\"\" ${\\cal M}\\sp\\prime$ of ${\\cal M}$ that runs in time o(T). We find that the answer is affirmative for a wide range of machine models, including the tree Turing machine, the multidimensional Turing machine, the log-cost RAM (random access machine), the unit-cost RAM, and the pointer machine. All previous speedup results either relied on the severe limitation on the storage structure of ${\\cal M}$ (e.g., ${\\cal M}\\sp\\prime$ was a Turing machine with linear tapes) or required that ${\\cal M}\\sp\\prime$ had a more versatile storage structure than ${\\cal M}$ (e.g., ${\\cal M}\\sp\\prime$ was a PRAM (parallel RAM), and ${\\cal M}$ was a Turing machine with linear tapes). It was unclear whether it was the parallelism or the restriction on the storage structures (or the combination of both) that realized such speedup. We remove the above restrictions on storage structures in previous results. We present speedup theorems where the storage medium of ${\\cal M}\\sp\\prime$ is the same as (or even weaker than) that of ${\\cal M}$. Hence, parallelism alone suffices to achieve a speedup. One implication is that there does not exist any recursive function that is \"\"inherently not parallelizable.\"\"\"","Made available in DSpace on 2011-05-07T11:57:13Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9543665.pdf: 3638359 bytes, checksum: 6b189a26abfab53b62a65de0656a5507 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:34:43Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:13:23-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["The power of parallel time"]}]}],"canonical_facts":{"dc:contributor":["Loui, Michael C."],"dc:creator":["Mak, Ka Ho"],"dc:date":["2011-05-07T11:57:13Z","10000-01-01","1995"],"dc:description":["\"In this thesis, we address the following question: Are parallel machines always faster than sequential machines? Our approach is to examine the common machine models of sequential computation. For each such machine ${\\cal M}$ that runs in time T, we determine whether it is possible to speed up ${\\cal M}$ by a \"\"parallel version\"\" ${\\cal M}\\sp\\prime$ of ${\\cal M}$ that runs in time o(T). We find that the answer is affirmative for a wide range of machine models, including the tree Turing machine, the multidimensional Turing machine, the log-cost RAM (random access machine), the unit-cost RAM, and the pointer machine. All previous speedup results either relied on the severe limitation on the storage structure of ${\\cal M}$ (e.g., ${\\cal M}\\sp\\prime$ was a Turing machine with linear tapes) or required that ${\\cal M}\\sp\\prime$ had a more versatile storage structure than ${\\cal M}$ (e.g., ${\\cal M}\\sp\\prime$ was a PRAM (parallel RAM), and ${\\cal M}$ was a Turing machine with linear tapes). It was unclear whether it was the parallelism or the restriction on the storage structures (or the combination of both) that realized such speedup. We remove the above restrictions on storage structures in previous results. We present speedup theorems where the storage medium of ${\\cal M}\\sp\\prime$ is the same as (or even weaker than) that of ${\\cal M}$. Hence, parallelism alone suffices to achieve a speedup. One implication is that there does not exist any recursive function that is \"\"inherently not parallelizable.\"\"\"","Made available in DSpace on 2011-05-07T11:57:13Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9543665.pdf: 3638359 bytes, checksum: 6b189a26abfab53b62a65de0656a5507 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:34:43Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:13:23-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9543665","(UMI)AAI9543665","http://hdl.handle.net/2142/19109"],"dc:language":["eng"],"dc:rights":["Copyright 1995 Mak, Ka Ho"],"dc:subject":["Computer Science"],"dc:title":["The power of parallel time"],"dc:type":["text"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:12Z"}