{"id":"https://openalex.org/W3136906194","doi":"https://doi.org/10.1109/lics.2017.8005100","title":"","display_name":"","publication_year":2017,"publication_date":"2017-08-18","ids":{"openalex":"https://openalex.org/W3136906194","doi":"https://doi.org/10.1109/lics.2017.8005100","mag":"3136906194"},"language":"en","primary_location":{"id":"pmh:oai:pure.ed.ac.uk:openaire/860e66fa-3ef0-4c33-80e4-b8a8e8307930","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/860e66fa-3ef0-4c33-80e4-b8a8e8307930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mayr, R, Kiefer, S, Shirmohammadi, M & Wojtczak, D 2017, Parity Objectives in Countable MDPs. in 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). Institute of Electrical and Electronics Engineers, 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, Reykjavik, Iceland, 20/06/17. https://doi.org/10.1109/LICS.2017.8005100","raw_type":"contributionToPeriodical"},"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/en/publications/860e66fa-3ef0-4c33-80e4-b8a8e8307930","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082358544","display_name":"Richard Mayr","orcid":"https://orcid.org/0009-0003-2164-9933"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210086594","display_name":"University Foundation","ror":"https://ror.org/001t02e86","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I4210086594"]}],"countries":["BE","GB"],"is_corresponding":false,"raw_author_name":"Richard Mayr","raw_affiliation_strings":["School of Informatics","Laboratory for Foundations of Computer Science","Foundations of Computation","University of Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Informatics","institution_ids":[]},{"raw_affiliation_string":"Laboratory for Foundations of Computer Science","institution_ids":[]},{"raw_affiliation_string":"Foundations of Computation","institution_ids":["https://openalex.org/I4210086594"]},{"raw_affiliation_string":"University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054782057","display_name":"Stefan Kiefer","orcid":"https://orcid.org/0000-0003-4173-6877"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stefan Kiefer","raw_affiliation_strings":["University of Oxford","University of Edinburgh, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"University of Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005502598","display_name":"Mahsa Shirmohammadi","orcid":"https://orcid.org/0000-0002-7779-2339"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mahsa Shirmohammadi","raw_affiliation_strings":["University of Oxford","University of Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001234060","display_name":"Dominik Wojtczak","orcid":"https://orcid.org/0000-0001-5560-0546"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]},{"id":"https://openalex.org/I4210155156","display_name":"Merseytravel","ror":"https://ror.org/05azmgh93","country_code":"GB","type":"government","lineage":["https://openalex.org/I4210155156"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Dominik Wojtczak","raw_affiliation_strings":["University of Liverpool","University of Liverpool, Liverpool, Merseyside, GB"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"University of Liverpool, Liverpool, Merseyside, GB","institution_ids":["https://openalex.org/I4210155156","https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":null,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9947999715805054,"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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9947999715805054,"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/T10142","display_name":"Formal Methods in Verification","score":0.9902999997138977,"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":0.9715999960899353,"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/reachability","display_name":"Reachability","score":0.8610403537750244},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.8511595726013184},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7102606296539307},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.6932346820831299},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6081587076187134},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46717721223831177},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45213523507118225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39623311161994934},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.25446969270706177},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08026835322380066}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8610403537750244},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.8511595726013184},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7102606296539307},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.6932346820831299},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6081587076187134},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46717721223831177},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45213523507118225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39623311161994934},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25446969270706177},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08026835322380066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:pure.ed.ac.uk:openaire/860e66fa-3ef0-4c33-80e4-b8a8e8307930","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/860e66fa-3ef0-4c33-80e4-b8a8e8307930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mayr, R, Kiefer, S, Shirmohammadi, M & Wojtczak, D 2017, Parity Objectives in Countable MDPs. in 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). Institute of Electrical and Electronics Engineers, 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, Reykjavik, Iceland, 20/06/17. https://doi.org/10.1109/LICS.2017.8005100","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:pure.ed.ac.uk:publications/860e66fa-3ef0-4c33-80e4-b8a8e8307930","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/portal/en/publications/parity-objectives-in-countable-mdps(860e66fa-3ef0-4c33-80e4-b8a8e8307930).html","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:openaire/860e66fa-3ef0-4c33-80e4-b8a8e8307930","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/860e66fa-3ef0-4c33-80e4-b8a8e8307930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mayr, R, Kiefer, S, Shirmohammadi, M & Wojtczak, D 2017, Parity Objectives in Countable MDPs. in 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). Institute of Electrical and Electronics Engineers, 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, Reykjavik, Iceland, 20/06/17. https://doi.org/10.1109/LICS.2017.8005100","raw_type":"contributionToPeriodical"},"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17"}],"awards":[{"id":"https://openalex.org/G3651020844","display_name":"Energy Efficient Control","funder_award_id":"EP/M027651/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4704183438","display_name":"EPSRC-Royal Society fellowship engagement (2013): Probabilistic Termination","funder_award_id":"EP/M003795/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4968910455","display_name":"Solving Parity Games in Theory and Practice","funder_award_id":"EP/P020909/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G772980944","display_name":"Energy Efficient Control","funder_award_id":"EP/M027287/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W135426567","https://openalex.org/W979688668","https://openalex.org/W1482647296","https://openalex.org/W1966347268","https://openalex.org/W2005684815","https://openalex.org/W2038680194","https://openalex.org/W2056099894","https://openalex.org/W2069791914","https://openalex.org/W2083816928","https://openalex.org/W2095414659","https://openalex.org/W2101561362","https://openalex.org/W2153399290","https://openalex.org/W2165161585","https://openalex.org/W2216663278","https://openalex.org/W2334782222","https://openalex.org/W2481607031","https://openalex.org/W2502103274","https://openalex.org/W2753908209","https://openalex.org/W4212845139","https://openalex.org/W4234607582","https://openalex.org/W4254547512"],"related_works":["https://openalex.org/W2127267268","https://openalex.org/W2156446763","https://openalex.org/W2136512912","https://openalex.org/W2067910792","https://openalex.org/W2150194458","https://openalex.org/W2143461633","https://openalex.org/W2889071233","https://openalex.org/W4321471459","https://openalex.org/W4221156924","https://openalex.org/W4300463216"],"abstract_inverted_index":{"We":[0],"study":[1],"countably":[2,47,159],"infinite":[3,48,59,116,148,160],"MDPs":[4,28,161],"with":[5,11],"parity":[6,38],"objectives,":[7,39],"and":[8,25],"special":[9],"cases":[10],"a":[12,63,86,151],"bounded":[13],"number":[14],"of":[15,66,70,93,158],"colors":[16],"in":[17,78,122],"the":[18,67,79,96,110,123,156],"Mostowski":[19,80,124],"hierarchy":[20],"(including":[21],"reachability,":[22],"safety,":[23],"Buchi":[24],"co-Buchi).<br/>In":[26],"finite":[27],"there":[29,84],"always":[30],"exist":[31],"optimal":[32,52,71,99,113],"memoryless":[33],"deterministic":[34],"(MD)":[35],"strategies":[36,53,74,114,129,134,146],"for":[37,46,75,109,119,143,155],"but":[40],"this":[41],"does":[42],"not":[43,55],"generally":[44],"hold":[45],"MDPs.":[49],"In":[50,82],"particular,":[51,83],"need":[54],"exist.":[56],"For":[57,95],"countable":[58],"MDPs,":[60],"we":[61],"provide":[62],"complete":[64],"picture":[65],"memory":[68],"requirements":[69],"(resp.,":[72],"\u03f5-optimal)":[73],"all":[76,120],"objectives":[77,121,138,168],"hierarchy.":[81],"is":[85],"strong":[87],"dichotomy":[88,152],"between":[89],"two":[90],"different":[91],"types":[92],"objectives.":[94],"first":[97],"type,":[98],"strategies,":[100],"if":[101,126],"they":[102],"exist,":[103],"can":[104],"be":[105],"chosen":[106],"MD,":[107],"while":[108,142],"second":[111],"type":[112],"require":[115,147],"memory.":[117,149],"(I.e.,":[118],"hierarchy,":[125],"finite-memory":[127],"randomized":[128],"suffice":[130],"then":[131],"also":[132,153],"MD":[133],"suffice.)":[135],"Similarly,":[136],"some":[137],"admit":[139,169],"\u03f5-optimal":[140,145],"MD-strategies,":[141],"others":[144],"Such":[150],"holds":[154],"subclass":[157],"that":[162],"are":[163],"finitely":[164],"branching,":[165],"though":[166],"more":[167],"MD-strategies":[170],"here.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
