{"id":"https://openalex.org/W7214639431","doi":"https://doi.org/10.48550/arxiv.2609.30817","title":"Quadratic bounds for uncompletable words and matrix mortality","display_name":"Quadratic bounds for uncompletable words and matrix mortality","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214639431","doi":"https://doi.org/10.48550/arxiv.2609.30817"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30817","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30817","pdf_url":"https://arxiv.org/pdf/2609.30817","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,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.30817","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153299124","display_name":"Rahul Chandelkar","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chandelkar, Rahul","raw_affiliation_strings":["Efficient Computation Inc "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Efficient Computation Inc ","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153323124","display_name":"Samrath Chadha","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chadha, Samrath Singh","raw_affiliation_strings":["Efficient Computation Inc "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Efficient Computation Inc ","institution_ids":[]}]}],"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":true,"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":0.9976000189781189,"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":0.9976000189781189,"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/T11269","display_name":"Algorithms and Data Compression","score":0.002199999988079071,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":9.999999747378752e-05,"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/kraft-inequality","display_name":"Kraft inequality","score":0.7409999966621399},{"id":"https://openalex.org/keywords/joint-spectral-radius","display_name":"joint spectral radius","score":0.6539999842643738},{"id":"https://openalex.org/keywords/zero-products","display_name":"zero products","score":0.6039999723434448},{"id":"https://openalex.org/keywords/strongly-connected-components","display_name":"strongly connected components","score":0.6399999856948853},{"id":"https://openalex.org/keywords/conditional-expectation","display_name":"conditional expectation","score":0.621999979019165},{"id":"https://openalex.org/keywords/polynomial-time-algorithms","display_name":"polynomial-time algorithms","score":0.5740000009536743},{"id":"https://openalex.org/keywords/lean-formal-verification","display_name":"Lean formal verification","score":0.5649999976158142}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8248999714851379},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8223999738693237},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.6503999829292297},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5293999910354614},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5289000272750854},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48030000925064087},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4724999964237213},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.45170000195503235},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.44369998574256897},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.43220001459121704},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.430400013923645},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.42719998955726624},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.4104999899864197},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4018999934196472},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.32820001244544983},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.30090001225471497},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.27379998564720154},{"id":"https://openalex.org/C85136909","wikidata":"https://www.wikidata.org/wiki/Q939272","display_name":"Incidence matrix","level":3,"score":0.27239999175071716},{"id":"https://openalex.org/C164804908","wikidata":"https://www.wikidata.org/wiki/Q2985058","display_name":"Combinatorics on words","level":3,"score":0.2685999870300293},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.30817","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30817","pdf_url":"https://arxiv.org/pdf/2609.30817","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,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.30817","doi":"https://doi.org/10.48550/arxiv.2609.30817","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30817","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.30817","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30817","pdf_url":"https://arxiv.org/pdf/2609.30817","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,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214639431.pdf","grobid_xml":"https://content.openalex.org/works/W7214639431.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2040416787","https://openalex.org/W2886677243","https://openalex.org/W2951118179","https://openalex.org/W2981188613","https://openalex.org/W3137903677"],"related_works":["https://openalex.org/W2886677243","https://openalex.org/W2040416787","https://openalex.org/W2921024523","https://openalex.org/W2095428245","https://openalex.org/W2941322157","https://openalex.org/W1536222145","https://openalex.org/W2071535502","https://openalex.org/W2749557323","https://openalex.org/W2774034339","https://openalex.org/W1667095670"],"abstract_inverted_index":{"Every":[0],"finite":[1,41],"nonempty":[2],"incomplete":[3],"uniquely":[4],"decipherable":[5],"code":[6],"with":[7,89,124],"maximum":[8],"word":[9,15,50],"length":[10,17,115,132],"$k$":[11],"has":[12,101,110,127],"an":[13,62],"uncompletable":[14,63],"of":[16,25,28,51,83,114,131],"at":[18,93,116],"most":[19,94,117],"$4k^2-3k$.":[20],"The":[21,139],"bound":[22,79],"is":[23],"independent":[24],"the":[26,68,78,135,142],"number":[27],"codewords":[29],"and":[30,57,71,141],"their":[31],"total":[32],"length.":[33],"Deleting":[34],"a":[35,40,48,102,108,111],"complete":[36],"codeword":[37],"cycle":[38],"gives":[39],"path-counting":[42],"identity;":[43],"Kraft":[44],"equality":[45],"then":[46],"supplies":[47],"short":[49],"deficient":[52],"compressed":[53],"mass.":[54],"Cyclic":[55],"averaging":[56],"padding":[58],"turn":[59],"it":[60],"into":[61],"word.":[64],"Conditional":[65],"expectation":[66],"makes":[67],"construction":[69],"polynomial-time":[70],"also":[72],"decides":[73],"completeness.":[74],"First-return":[75],"words":[76],"extend":[77],"to":[80],"mortal":[81],"families":[82],"nonnegative":[84],"integer":[85],"$n\\times":[86],"n$":[87],"matrices":[88],"joint":[90],"spectral":[91],"radius":[92],"one,":[95],"provided":[96],"every":[97,105],"strongly":[98],"connected":[99],"component":[100],"vertex":[103],"meeting":[104],"cycle.":[106],"Such":[107],"family":[109,123],"zero":[112,129],"product":[113,130],"$4n^2-3n$.":[118],"A":[119],"binary":[120],"partial":[121],"deterministic":[122],"$2k-1$":[125],"states":[126],"shortest":[128],"$k^2+k-1$,":[133],"establishing":[134],"optimal":[136],"quadratic":[137],"order.":[138],"bounds":[140],"explicit-code":[143],"algorithm,":[144],"including":[145],"its":[146],"polynomial":[147],"work":[148],"bound,":[149],"are":[150],"proved":[151],"in":[152],"Lean.":[153]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-29T00:00:00"}
