{"id":"https://openalex.org/W3167488367","doi":"https://doi.org/10.25972/opus-22220","title":"Balance Problems for Integer Circuits and Separations of Relativized Conjectures on Incompleteness in Promise Classes","display_name":"Balance Problems for Integer Circuits and Separations of Relativized Conjectures on Incompleteness in Promise Classes","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3167488367","doi":"https://doi.org/10.25972/opus-22220","mag":"3167488367"},"language":"en","primary_location":{"id":"pmh:oai:opus.bibliothek.uni-wuerzburg.de:22220","is_oa":true,"landing_page_url":"https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/22220","pdf_url":"https://opus.bibliothek.uni-wuerzburg.de/files/22220/Dose_Titus_BalanceProblems.pdf","source":{"id":"https://openalex.org/S4306401635","display_name":"Online Publication Service of W\u00fcrzburg University (W\u00fcrzburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I25974101","host_organization_name":"University of W\u00fcrzburg","host_organization_lineage":["https://openalex.org/I25974101"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:doctoralThesis"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://opus.bibliothek.uni-wuerzburg.de/files/22220/Dose_Titus_BalanceProblems.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031545851","display_name":"Titus Dose","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dose, Titus","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031545851"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10329678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9772999882698059,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9772999882698059,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.955299973487854,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9355000257492065,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.8083385229110718},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7022762298583984},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6544184684753418},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6496129035949707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6340508460998535},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5529454350471497},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.5412508845329285},{"id":"https://openalex.org/keywords/constraint-satisfaction-problem","display_name":"Constraint satisfaction problem","score":0.5377889275550842},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.4939115643501282},{"id":"https://openalex.org/keywords/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.46063506603240967},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42013415694236755},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1536596417427063}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.8083385229110718},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7022762298583984},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6544184684753418},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6496129035949707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6340508460998535},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5529454350471497},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.5412508845329285},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.5377889275550842},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.4939115643501282},{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.46063506603240967},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42013415694236755},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1536596417427063},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:opus.bibliothek.uni-wuerzburg.de:22220","is_oa":true,"landing_page_url":"https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/22220","pdf_url":"https://opus.bibliothek.uni-wuerzburg.de/files/22220/Dose_Titus_BalanceProblems.pdf","source":{"id":"https://openalex.org/S4306401635","display_name":"Online Publication Service of W\u00fcrzburg University (W\u00fcrzburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I25974101","host_organization_name":"University of W\u00fcrzburg","host_organization_lineage":["https://openalex.org/I25974101"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:doctoralThesis"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-032630061","is_oa":false,"landing_page_url":"https://doi.org/10.25972/OPUS-22220","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.25972/opus-22220","is_oa":true,"landing_page_url":"https://doi.org/10.25972/opus-22220","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"thesis"},{"id":"mag:3167488367","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-wuerzburg.de/files/22220/Dose_Titus_BalanceProblems.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:opus.bibliothek.uni-wuerzburg.de:22220","is_oa":true,"landing_page_url":"https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/22220","pdf_url":"https://opus.bibliothek.uni-wuerzburg.de/files/22220/Dose_Titus_BalanceProblems.pdf","source":{"id":"https://openalex.org/S4306401635","display_name":"Online Publication Service of W\u00fcrzburg University (W\u00fcrzburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I25974101","host_organization_name":"University of W\u00fcrzburg","host_organization_lineage":["https://openalex.org/I25974101"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:doctoralThesis"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3167488367.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2970049274","https://openalex.org/W3000303691","https://openalex.org/W2966442607","https://openalex.org/W2626569379","https://openalex.org/W1969813680","https://openalex.org/W2008585307","https://openalex.org/W753286845","https://openalex.org/W2053175898","https://openalex.org/W2119677808","https://openalex.org/W3170426943","https://openalex.org/W3041052328","https://openalex.org/W1998964055","https://openalex.org/W2791077999","https://openalex.org/W1967048340","https://openalex.org/W2524078459","https://openalex.org/W2039931384","https://openalex.org/W2913548468","https://openalex.org/W3004454050","https://openalex.org/W1547393828","https://openalex.org/W42931805"],"abstract_inverted_index":{"This":[0],"thesis":[1],"is":[2,200,203,223],"divided":[3],"into":[4],"two":[5],"parts.":[6],"In":[7,137],"the":[8,131,138,143,161,195,204,235,255],"first":[9,205],"part":[10,140],"we":[11,141,232],"contribute":[12],"to":[13,29,225,249],"a":[14],"working":[15],"program":[16],"initiated":[17],"by":[18,177],"Pudl\u00e1k":[19,134],"(2017)":[20],"who":[21],"lists":[22],"several":[23,129],"major":[24],"complexity":[25,31,145,236],"theoretic":[26],"conjectures":[27,45],"relevant":[28],"proof":[30,62,75],"and":[32,49,97,173,179,183,186,222,259],"asks":[33,135],"for":[34,149,170,198,208,240,252],"oracles":[35,132],"that":[36,59,72,133,158,194,216],"separate":[37],"pairs":[38,106],"of":[39,130,146,154,237,243,254],"corresponding":[40],"relativized":[41],"conjectures.":[42],"Among":[43],"these":[44],"are:":[46],"-":[47,64,77,95,109,117,125],"\\(\\mathsf{CON}\\)":[48],"\\(\\mathsf{SAT}\\):":[50],"coNP":[51,66],"(resp.,":[52],"NP)":[53],"does":[54,67,112,120],"not":[55,68,81,101,113,121],"contain":[56,69,114,122],"complete":[57,70,83,103,115,123,251],"sets":[58,71,153],"have":[60,73],"P-optimal":[61],"systems.":[63,76],"\\(\\mathsf{CON}^{\\mathsf{N}}\\):":[65],"optimal":[74],"\\(\\mathsf{TFNP}\\):":[78],"there":[79],"do":[80,100],"exist":[82,102],"total":[84,91],"polynomial":[85],"search":[86,93],"problems":[87,148,165,169,215,239,246],"(also":[88],"known":[89],"as":[90],"NP":[92,105],"problems).":[94],"\\(\\mathsf{DisjNP}\\)":[96],"\\(\\mathsf{DisjCoNP}\\):":[98],"There":[99],"disjoint":[104],"(coNP":[107],"pairs).":[108],"\\(\\mathsf{UP}\\):":[110],"UP":[111],"problems.":[116,124],"\\(\\mathsf{NP}\\cap\\mathsf{coNP}\\):":[118],"\\(\\mathrm{NP}\\cap\\mathrm{coNP}\\)":[119],"\\(\\mathrm{P}\\ne\\mathrm{NP}\\).":[126],"We":[127],"construct":[128],"for.":[136],"second":[139],"investigate":[142],"computational":[144],"balance":[147,196,238],"\\(\\{-,\\cdot\\}\\)-circuits":[150,199],"computing":[151],"finite":[152],"natural":[155,206],"numbers":[156],"(note":[157],"\\(-\\)":[159],"denotes":[160],"set":[162],"difference).":[163],"These":[164,245],"naturally":[166],"build":[167],"on":[168],"integer":[171,174,209],"expressions":[172],"circuits":[175,210],"studied":[176],"Stockmeyer":[178],"Meyer":[180],"(1973),":[181],"McKenzie":[182],"Wagner":[184],"(2007),":[185],"Gla\u00dfer":[187],"et":[188],"al.":[189],"(2010).":[190],"Our":[191],"work":[192],"shows":[193],"problem":[197,207],"undecidable":[201],"which":[202],"or":[211],"related":[212],"constraint":[213],"satisfaction":[214],"admits":[217],"only":[218],"one":[219,253],"arithmetic":[220],"operation":[221],"proven":[224],"be":[226,250],"undecidable.":[227],"Starting":[228],"from":[229],"this":[230],"result":[231],"precisely":[233],"characterize":[234],"proper":[241],"subsets":[242],"\\(\\{-,\\cdot\\}\\).":[244],"turn":[247],"out":[248],"classes":[256],"L,":[257],"NL,":[258],"NP.":[260]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}