{"id":"https://openalex.org/W7161948382","doi":"https://doi.org/10.48550/arxiv.2605.20421","title":"Intersecting Dense Automata","display_name":"Intersecting Dense Automata","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W7161948382","doi":"https://doi.org/10.48550/arxiv.2605.20421"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.20421","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.20421","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.2605.20421","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123119033","display_name":"Dmitry Chistikov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chistikov, Dmitry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5088843055","display_name":"Neha Rino","orcid":"https://orcid.org/0009-0001-3273-1954"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rino, Neha","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/T11567","display_name":"semigroups and automata theory","score":0.5246999859809875,"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/T11567","display_name":"semigroups and automata theory","score":0.5246999859809875,"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/T10142","display_name":"Formal Methods in Verification","score":0.31869998574256897,"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/T12029","display_name":"DNA and Biological Computing","score":0.05420000106096268,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.7497000098228455},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7451000213623047},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.6291999816894531},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.5659999847412109},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.4991999864578247},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4693000018596649},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.3601999878883362}],"concepts":[{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.7497000098228455},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7451000213623047},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.6291999816894531},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5659999847412109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5591999888420105},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.512499988079071},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.4991999864578247},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4693000018596649},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4372999966144562},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40689998865127563},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.3601999878883362},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.3582000136375427},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31049999594688416},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30880001187324524},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.25949999690055847}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.20421","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.20421","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.2605.20421","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.20421","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":{"We":[0,55],"observe":[1],"that":[2],"the":[3,9,21,25,34,67],"classical":[4],"Cartesian":[5],"product":[6,35],"construction":[7],"for":[8,66,85,102,117],"intersection":[10,68,88,119],"of":[11,36,69],"(languages":[12],"of)":[13],"nondeterministic":[14],"finite":[15],"automata":[16,26],"(NFA)":[17],"is":[18,93],"non-optimal":[19],"in":[20,105],"worst":[22],"case,":[23],"if":[24,43],"have":[27,40,46],"many":[28],"transitions.":[29],"For":[30],"a":[31,82,98,112],"fixed":[32,73],"alphabet,":[33],"two":[37],"NFA":[38,45,71,87,118],"may":[39],"$\u0398(m^2)$":[41],"transitions":[42,53],"these":[44],"at":[47],"most":[48],"$n$":[49],"states":[50],"and":[51,77],"$m$":[52],"each.":[54],"describe":[56],"alternative":[57],"constructions":[58],"with":[59],"$O(m":[60,64],"n)$":[61],"transitions:":[62],"or":[63],"n^{k-1})$":[65],"$k$":[70],"(for":[72],"$k":[74],"\\ge":[75],"2$":[76],"alphabet":[78],"$\u03a3$).":[79],"This":[80,108],"gives":[81],"faster":[83],"algorithm":[84,92,101],"deciding":[86],"emptiness.":[89,120],"The":[90],"new":[91],"optimal,":[94],"unless":[95],"there":[96],"exists":[97],"breakthrough":[99],"combinatorial":[100],"detecting":[103],"$(k+1)$-cliques":[104],"undirected":[106],"graphs.":[107],"also":[109],"leads":[110],"to":[111],"more":[113],"efficient":[114],"certification":[115],"scheme":[116]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-22T00:00:00"}
