{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71229"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71229","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Alternation and Omega-Type Turing Acceptors","abstract":"An (omega)-language is a set of infinite ((omega)-type) strings of symbols. We study the classes of (omega)-languages accepted by Turing Acceptors when infinite computations are allowed. There are various possible "natural" acceptance conditions to consider, including those already common in the literature of (omega)-automata. There are also the deterministic (D), nondeterministic (N) and alternating (A) models to consider. Alternating machines were introduced by Chandra, Kozen and Stockmeyer (J. Assoc. Comp. Mach. 28 (1981), 114-133) as a natural extension of nondeterministic machines. (In symbols: D (LESSTHEQ) N (LESSTHEQ) A.)","abstract_html":"An (omega)-language is a set of infinite ((omega)-type) strings of symbols. We study the classes of (omega)-languages accepted by Turing Acceptors when infinite computations are allowed. There are various possible "natural" acceptance conditions to consider, including those already common in the literature of (omega)-automata. There are also the deterministic (D), nondeterministic (N) and alternating (A) models to consider. Alternating machines were introduced by Chandra, Kozen and Stockmeyer (J. Assoc. Comp. Mach. 28 (1981), 114-133) as a natural extension of nondeterministic machines. (In symbols: D (LESSTHEQ) N (LESSTHEQ) A.)","abstract_has_math":false,"creators":["Lindsay, Peter Alexander"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:12Z","date_published":"2014-12-16T06:18:12Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8502221"],"render_values":[{"text":"(UMI)AAI8502221","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71229","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Lindsay, Peter Alexander"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:12Z","10000-01-01","1984"]},{"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":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71229","(UMI)AAI8502221"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["An (omega)-language is a set of infinite ((omega)-type) strings of symbols. We study the classes of (omega)-languages accepted by Turing Acceptors when infinite computations are allowed. There are various possible "natural" acceptance conditions to consider, including those already common in the literature of (omega)-automata. There are also the deterministic (D), nondeterministic (N) and alternating (A) models to consider. Alternating machines were introduced by Chandra, Kozen and Stockmeyer (J. Assoc. Comp. Mach. 28 (1981), 114-133) as a natural extension of nondeterministic machines. (In symbols: D (LESSTHEQ) N (LESSTHEQ) A.)","It is seen that under certain acceptance conditions alternating (omega)-TA's are no more powerful than their nondeterministic counterparts, while under other conditions they are far more powerful. In fact, each of the following cases occurs: D < N < A; D = N < A; D < N = A. We characterize the classes in terms of the arithmetical and analytical hierarchies of (omega)-languages (c.f. Rogers, Theory of Recursive Functions and Effective Computability, chapter 14) and give examples of (omega)-languages which are in some sense the most complicated in each class.","Made available in DSpace on 2014-12-16T06:18:12Z (GMT). No. of bitstreams: 1 8502221.pdf: 2391355 bytes, checksum: 7380815aaef9ebc6edef4db6c9243fa0 (MD5) Previous issue date: 1984","Embargo set by: Seth Robbins for item 71395 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","103 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984."]},{"key":"dc:title","label":"Title","values":["Alternation and Omega-Type Turing Acceptors"]}]}],"canonical_facts":{"dc:creator":["Lindsay, Peter Alexander"],"dc:date":["2014-12-16T06:18:12Z","10000-01-01","1984"],"dc:description":["An (omega)-language is a set of infinite ((omega)-type) strings of symbols. We study the classes of (omega)-languages accepted by Turing Acceptors when infinite computations are allowed. There are various possible "natural" acceptance conditions to consider, including those already common in the literature of (omega)-automata. There are also the deterministic (D), nondeterministic (N) and alternating (A) models to consider. Alternating machines were introduced by Chandra, Kozen and Stockmeyer (J. Assoc. Comp. Mach. 28 (1981), 114-133) as a natural extension of nondeterministic machines. (In symbols: D (LESSTHEQ) N (LESSTHEQ) A.)","It is seen that under certain acceptance conditions alternating (omega)-TA's are no more powerful than their nondeterministic counterparts, while under other conditions they are far more powerful. In fact, each of the following cases occurs: D < N < A; D = N < A; D < N = A. We characterize the classes in terms of the arithmetical and analytical hierarchies of (omega)-languages (c.f. Rogers, Theory of Recursive Functions and Effective Computability, chapter 14) and give examples of (omega)-languages which are in some sense the most complicated in each class.","Made available in DSpace on 2014-12-16T06:18:12Z (GMT). No. of bitstreams: 1 8502221.pdf: 2391355 bytes, checksum: 7380815aaef9ebc6edef4db6c9243fa0 (MD5) Previous issue date: 1984","Embargo set by: Seth Robbins for item 71395 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","103 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984."],"dc:identifier":["http://hdl.handle.net/2142/71229","(UMI)AAI8502221"],"dc:subject":["Mathematics"],"dc:title":["Alternation and Omega-Type Turing Acceptors"],"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":"2026-07-22T22:26:04Z"}