{"id":"https://openalex.org/W2070046126","doi":"https://doi.org/10.1080/15427951.2008.10129176","title":"Atropos: A PSPACE-Complete Sperner Triangle Game","display_name":"Atropos: A PSPACE-Complete Sperner Triangle Game","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2070046126","doi":"https://doi.org/10.1080/15427951.2008.10129176","mag":"2070046126"},"language":"en","primary_location":{"id":"doi:10.1080/15427951.2008.10129176","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2008.10129176","pdf_url":"https://www.internetmathematicsjournal.com/article/1473.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.internetmathematicsjournal.com/article/1473.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036070557","display_name":"Kyle Burke","orcid":"https://orcid.org/0000-0002-9222-8832"},"institutions":[{"id":"https://openalex.org/I18860807","display_name":"Wittenberg University","ror":"https://ror.org/04a23br85","country_code":"US","type":"education","lineage":["https://openalex.org/I18860807"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kyle W. Burke","raw_affiliation_strings":["Department of Mathematics and Computer Science, Wittenberg University, P. O. Box 720, Springfield, OH 45501"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Wittenberg University, P. O. Box 720, Springfield, OH 45501","institution_ids":["https://openalex.org/I18860807"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102005063","display_name":"Shang\u2010Hua Teng","orcid":"https://orcid.org/0000-0001-5011-4514"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shang-Hua Teng","raw_affiliation_strings":["Viterbi School of Engineering, University of Southern California, 941 Bloom Walk, Los Angeles, CA 90089"],"affiliations":[{"raw_affiliation_string":"Viterbi School of Engineering, University of Southern California, 941 Bloom Walk, Los Angeles, CA 90089","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036070557"],"corresponding_institution_ids":["https://openalex.org/I18860807"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.13893606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"5","issue":"4","first_page":"477","last_page":"492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9702000021934509,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9656000137329102,"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/mathematics","display_name":"Mathematics","score":0.7031266093254089},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6611835956573486},{"id":"https://openalex.org/keywords/combinatorial-game-theory","display_name":"Combinatorial game theory","score":0.5811828374862671},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5493086576461792},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.5213914513587952},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.46096986532211304},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4472358524799347},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.43921995162963867},{"id":"https://openalex.org/keywords/meaning","display_name":"Meaning (existential)","score":0.4300704598426819},{"id":"https://openalex.org/keywords/screening-game","display_name":"Screening game","score":0.4205082654953003},{"id":"https://openalex.org/keywords/simultaneous-game","display_name":"Simultaneous game","score":0.4134674370288849},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39295634627342224},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33438414335250854},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.29285573959350586},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.2320357859134674},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.14972808957099915},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10177150368690491}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7031266093254089},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6611835956573486},{"id":"https://openalex.org/C102234262","wikidata":"https://www.wikidata.org/wiki/Q1320931","display_name":"Combinatorial game theory","level":4,"score":0.5811828374862671},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5493086576461792},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.5213914513587952},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.46096986532211304},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4472358524799347},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.43921995162963867},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.4300704598426819},{"id":"https://openalex.org/C167573328","wikidata":"https://www.wikidata.org/wiki/Q7439054","display_name":"Screening game","level":4,"score":0.4205082654953003},{"id":"https://openalex.org/C95940807","wikidata":"https://www.wikidata.org/wiki/Q12237274","display_name":"Simultaneous game","level":4,"score":0.4134674370288849},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39295634627342224},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33438414335250854},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.29285573959350586},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.2320357859134674},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.14972808957099915},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10177150368690491},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/15427951.2008.10129176","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2008.10129176","pdf_url":"https://www.internetmathematicsjournal.com/article/1473.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.im/1265033176","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.im/1265033176","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1080/15427951.2008.10129176","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2008.10129176","pdf_url":"https://www.internetmathematicsjournal.com/article/1473.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6646512391","display_name":"IGERT:  Multidisciplinary Integration of High Performance Computing in Ph. D. Programs in Science and Engineering","funder_award_id":"0221680","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8519613297","display_name":null,"funder_award_id":"DGE-0221680","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2070046126.pdf","grobid_xml":"https://content.openalex.org/works/W2070046126.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1498333122","https://openalex.org/W1574089563","https://openalex.org/W1973474784","https://openalex.org/W2021445310","https://openalex.org/W2026177035","https://openalex.org/W2027621512","https://openalex.org/W2083639782","https://openalex.org/W2140790422","https://openalex.org/W2156827107","https://openalex.org/W2169359757","https://openalex.org/W2840095145","https://openalex.org/W2950369663","https://openalex.org/W4230874062","https://openalex.org/W4234400829","https://openalex.org/W4289754022","https://openalex.org/W6651186454"],"related_works":["https://openalex.org/W1557018980","https://openalex.org/W4221159562","https://openalex.org/W2039104542","https://openalex.org/W2990217081","https://openalex.org/W2067232667","https://openalex.org/W4285034325","https://openalex.org/W4287102171","https://openalex.org/W2032375758","https://openalex.org/W4205287490","https://openalex.org/W47369278"],"abstract_inverted_index":{"We":[0,71],"create":[1],"Atropos,":[2],"a":[3,27,63,68,73],"new":[4],"two-player":[5],"game":[6,12,31,64],"based":[7,89],"on":[8,90],"Sperner's":[9],"lemma.":[10],"Our":[11],"has":[13],"simple":[14],"rules":[15],"and":[16,53],"several":[17],"desirable":[18],"properties.":[19],"First,":[20],"Atropos":[21,66],"is":[22,32,67],"always":[23,38],"certain":[24],"to":[25],"have":[26],"winner.":[28],"Second,":[29],"the":[30,41,77],"impartial,":[33],"meaning":[34],"that":[35,57],"both":[36],"players":[37],"can":[39,61],"make":[40],"same":[42],"moves.":[43],"Third,":[44],"like":[45],"many":[46],"other":[47,86],"interesting":[48],"games":[49],"such":[50],"as":[51],"Hex":[52],"geography,":[54],"we":[55,84],"prove":[56],"deciding":[58],"whether":[59],"one":[60],"win":[62],"of":[65,76],"PSPACE-complete":[69],"problem.":[70],"provide":[72],"web-based":[74],"version":[75],"game,":[78],"playable":[79],"at":[80],"http://cs-people.bu.edu/paithan/atropos/.":[81],"In":[82],"addition,":[83],"propose":[85],"games,":[87],"also":[88],"fixed-point":[91],"theorems.":[92]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}