{"id":"https://openalex.org/W7082627657","doi":"https://doi.org/10.4230/lipics.itp.2025.24","title":"Formally Verifying a Vertical Cell Decomposition Algorithm","display_name":"Formally Verifying a Vertical Cell Decomposition Algorithm","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W7082627657","doi":"https://doi.org/10.4230/lipics.itp.2025.24"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:24622","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.24","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol352-itp2025/LIPIcs.ITP.2025.24/LIPIcs.ITP.2025.24.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":null,"raw_type":"publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol352-itp2025/LIPIcs.ITP.2025.24/LIPIcs.ITP.2025.24.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Bertot, Yves","orcid":"https://orcid.org/0000-0001-5052-3019"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210144177","display_name":"Cognition Behaviour Technology","ror":"https://ror.org/04d9wv909","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210144177"]},{"id":"https://openalex.org/I4210149294","display_name":"Institut de Physique de Nice","ror":"https://ror.org/042cesy50","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210149294"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Bertot, Yves","raw_affiliation_strings":["Inria Center at Universit\u00e9 C\u00f4te d'Azur, Nice, France"],"raw_orcid":"https://orcid.org/0000-0001-5052-3019","affiliations":[{"raw_affiliation_string":"Inria Center at Universit\u00e9 C\u00f4te d'Azur, Nice, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210144177","https://openalex.org/I4210149294"]}]},{"author_position":"last","author":{"id":null,"display_name":"Portet, Thomas","orcid":"https://orcid.org/0009-0002-6258-8084"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210144177","display_name":"Cognition Behaviour Technology","ror":"https://ror.org/04d9wv909","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210144177"]},{"id":"https://openalex.org/I4210149294","display_name":"Institut de Physique de Nice","ror":"https://ror.org/042cesy50","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210149294"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Portet, Thomas","raw_affiliation_strings":["Inria Center at Universit\u00e9 C\u00f4te d'Azur, Nice, France"],"raw_orcid":"https://orcid.org/0009-0002-6258-8084","affiliations":[{"raw_affiliation_string":"Inria Center at Universit\u00e9 C\u00f4te d'Azur, Nice, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210144177","https://openalex.org/I4210149294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210144177","https://openalex.org/I4210149294"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.67249481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.367000013589859,"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/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.367000013589859,"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/T13177","display_name":"Geological and Geophysical Studies","score":0.05389999970793724,"subfield":{"id":"https://openalex.org/subfields/1907","display_name":"Geology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13067","display_name":"Geological Modeling and Analysis","score":0.028999999165534973,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.8152999877929688},{"id":"https://openalex.org/keywords/formal-proof","display_name":"Formal proof","score":0.6116999983787537},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5928000211715698},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4733000099658966},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.454800009727478},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.43689998984336853},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.3991999924182892},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32910001277923584}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.8152999877929688},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6243000030517578},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.6116999983787537},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5928000211715698},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5490999817848206},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4733000099658966},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.43689998984336853},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4291999936103821},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.3991999924182892},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39719998836517334},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.32179999351501465},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.31619998812675476},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.2888000011444092},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.26809999346733093}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:24622","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.24","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol352-itp2025/LIPIcs.ITP.2025.24/LIPIcs.ITP.2025.24.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:HAL:hal-05444842v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-05444842","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","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":"ITP 2025 - 16th International Conference on Interactive Theorem Proving, Sep 2025, Reykjavik, Iceland. pp.24, ⟨10.4230/LIPIcs.ITP.2025.24⟩","raw_type":"Conference papers"},{"id":"doi:10.4230/lipics.itp.2025.24","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.itp.2025.24","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:24622","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.24","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol352-itp2025/LIPIcs.ITP.2025.24/LIPIcs.ITP.2025.24.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.44016167521476746}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7082627657.pdf","grobid_xml":"https://content.openalex.org/works/W7082627657.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,113],"broad":[1],"context":[2],"of":[3,9,30,60,64,85,92,121],"this":[4,38,57,101],"work":[5],"is":[6,40,58],"the":[7,34,61,83,93,118],"application":[8],"formal":[10,35],"methods":[11],"to":[12,20,50,68,99,111],"geometry":[13],"and":[14,33,109],"robotics.":[15],"We":[16,42],"describe":[17],"an":[18,45,66],"algorithm":[19,39,46,67],"decompose":[21,69],"a":[22,28,70,128],"working":[23,71,94],"area":[24],"containing":[25],"obstacles":[26],"into":[27,73],"collection":[29],"safe":[31,52],"cells":[32,75],"proof":[36,84,102],"that":[37,76,87,89],"correct.":[41],"expect":[43],"such":[44,65],"will":[47],"be":[48],"useful":[49],"compute":[51],"trajectories.":[53],"To":[54],"our":[55],"knowledge,":[56],"one":[59],"first":[62],"formalization":[63],"space":[72,95],"elementary":[74],"are":[77,96,125],"suitable":[78],"for":[79],"later":[80],"applications,":[81],"with":[82],"correctness":[86],"guarantees":[88],"large":[90],"parts":[91],"safe.":[97],"Techniques":[98],"perform":[100],"go":[103],"from":[104,117],"algebraic":[105],"reasoning":[106],"on":[107],"coordinates":[108],"determinants":[110],"sorting.":[112],"main":[114],"difficulty":[115],"comes":[116],"possible":[119],"existence":[120],"degenerate":[122],"cases,":[123],"which":[124],"treated":[126],"in":[127],"principled":[129],"way.":[130]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}