{"id":"https://openalex.org/W7165960607","doi":"https://doi.org/10.48550/arxiv.2606.25276","title":"Decidability and Undecidability Results for LIA-Definable Impartial Combinatorial Games","display_name":"Decidability and Undecidability Results for LIA-Definable Impartial Combinatorial Games","publication_year":2026,"publication_date":"2026-06-24","ids":{"openalex":"https://openalex.org/W7165960607","doi":"https://doi.org/10.48550/arxiv.2606.25276"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.25276","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25276","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.25276","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013723834","display_name":"Shiguang Feng","orcid":"https://orcid.org/0000-0002-5110-3881"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Feng, Shiguang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139346320","display_name":"Liangda Fang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fang, Liangda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135410506","display_name":"Jiahao Luo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Jiahao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139360930","display_name":"Quanlong Guan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guan, Quanlong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T10142","display_name":"Formal Methods in Verification","score":0.6123999953269958,"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/T10142","display_name":"Formal Methods in Verification","score":0.6123999953269958,"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/T10126","display_name":"Logic, programming, and type systems","score":0.11630000174045563,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.05169999971985817,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.9864000082015991},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.953000009059906},{"id":"https://openalex.org/keywords/normalization-property","display_name":"Normalization property","score":0.7950999736785889},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4514000117778778},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.41760000586509705},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.40880000591278076}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.9864000082015991},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.953000009059906},{"id":"https://openalex.org/C159333733","wikidata":"https://www.wikidata.org/wiki/Q7051809","display_name":"Normalization property","level":2,"score":0.7950999736785889},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6067000031471252},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5806999802589417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.545199990272522},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4514000117778778},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.41760000586509705},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.3359000086784363},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29330000281333923},{"id":"https://openalex.org/C137343475","wikidata":"https://www.wikidata.org/wiki/Q622849","display_name":"Halting problem","level":4,"score":0.26339998841285706},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.25760000944137573}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.25276","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25276","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.25276","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25276","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Combinatorial":[0],"game":[1],"theory":[2],"is":[3,63,67,104,121,145,151],"a":[4,119,143],"branch":[5],"of":[6,22,26,94,100],"mathematics":[7],"and":[8,19,31,49,108,155],"theoretical":[9],"computer":[10],"science":[11],"that":[12,57,84],"studies":[13,47],"deterministic":[14],"games":[15,28,43],"with":[16],"perfect":[17],"information":[18],"no":[20],"elements":[21],"chance.":[23],"The":[24],"majority":[25],"combinatorial":[27,42],"are":[29],"impartial":[30,41],"formalized":[32],"in":[33,69,106,153],"linear":[34],"integer":[35],"arithmetic,":[36],"which":[37],"we":[38],"call":[39],"LIA-definable":[40,61,79,102,112,130,138,149,159],"(ICGs).":[44],"This":[45],"paper":[46],"decidability":[48],"undecidability":[50],"questions":[51,74],"for":[52,77,110,128,135,147,157],"these":[53],"games.":[54],"We":[55,81],"prove":[56],"deciding":[58,85,117,141],"whether":[59,86,118,142],"an":[60,87,101,148],"ICG":[62,103,150],"terminating":[64,78,111,129,136,158],"or":[65,97,123],"cyclic":[66],"undecidable":[68,105,126,152],"general,":[70],"while":[71],"the":[72,92],"corresponding":[73],"become":[75],"decidable":[76,109,134,156],"ICGs.":[80,113,139,160],"also":[82],"show":[83],"LIA":[88],"formula":[89],"exactly":[90],"characterizes":[91],"set":[93],"winning,":[95],"losing,":[96],"draw":[98,146],"states":[99],"general":[107,154],"For":[114],"state-level":[115],"questions,":[116],"state":[120,144],"winning":[122],"losing":[124],"remains":[125],"even":[127],"ICGs,":[131],"but":[132],"becomes":[133],"finite-depth":[137],"Finally,":[140]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-26T00:00:00"}
