{"id":"https://openalex.org/W4399360105","doi":"https://doi.org/10.46298/lmcs-20(2:11)2024","title":"On Robustness for the Skolem, Positivity and Ultimate Positivity Problems","display_name":"On Robustness for the Skolem, Positivity and Ultimate Positivity Problems","publication_year":2024,"publication_date":"2024-06-05","ids":{"openalex":"https://openalex.org/W4399360105","doi":"https://doi.org/10.46298/lmcs-20(2:11)2024"},"language":"en","primary_location":{"id":"doi:10.46298/lmcs-20(2:11)2024","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-20(2:11)2024","pdf_url":"https://lmcs.episciences.org/13724/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/13724/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063753055","display_name":"S. Akshay","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"S. Akshay","raw_affiliation_strings":["IIT Bombay - Indian Institute of Technology Bombay (Powai, Mumbai - 400076, India - India)"],"affiliations":[{"raw_affiliation_string":"IIT Bombay - Indian Institute of Technology Bombay (Powai, Mumbai - 400076, India - India)","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061027622","display_name":"Hugo Bazille","orcid":null},"institutions":[{"id":"https://openalex.org/I4210138808","display_name":"\u00c9cole Pour l'Informatique et les Techniques Avanc\u00e9es","ror":"https://ror.org/04r5ddq29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210138808"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Hugo Bazille","raw_affiliation_strings":["LRE - Laboratoire de Recherche de l'EPITA (14-16, RUE VOLTAIRE\r\n94270 LE KREMLIN-BIC\u00caTRE\r\nFRANCE - France)"],"affiliations":[{"raw_affiliation_string":"LRE - Laboratoire de Recherche de l'EPITA (14-16, RUE VOLTAIRE\r\n94270 LE KREMLIN-BIC\u00caTRE\r\nFRANCE - France)","institution_ids":["https://openalex.org/I4210138808"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064810861","display_name":"Blaise Genest","orcid":"https://orcid.org/0000-0002-5758-1876"},"institutions":[{"id":"https://openalex.org/I3005327000","display_name":"Institute for Infocomm Research","ror":"https://ror.org/053rfa017","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3005327000","https://openalex.org/I91275662"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Blaise Genest","raw_affiliation_strings":["CNRS@CREATE Ltd. (Singapore)","IPAL - Image & Pervasive Access Lab (Institute for Infocomm Research 1 Fusionopolis Way #21-01 Connexis (South Tower) Singapore 138632 - Singapore)"],"affiliations":[{"raw_affiliation_string":"CNRS@CREATE Ltd. (Singapore)","institution_ids":[]},{"raw_affiliation_string":"IPAL - Image & Pervasive Access Lab (Institute for Infocomm Research 1 Fusionopolis Way #21-01 Connexis (South Tower) Singapore 138632 - Singapore)","institution_ids":["https://openalex.org/I3005327000"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088140140","display_name":"Mihir Vahanwala","orcid":"https://orcid.org/0009-0008-5709-899X"},"institutions":[{"id":"https://openalex.org/I4210121786","display_name":"Max Planck Institute for Software Systems","ror":"https://ror.org/02pe2kf23","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210121786"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mihir Vahanwala","raw_affiliation_strings":["MPI-SWS - Max Planck Institute for Software Systems (D-66111 Saarbr\u00fccken/D-67663 Kaiserslautern - Germany)"],"affiliations":[{"raw_affiliation_string":"MPI-SWS - Max Planck Institute for Software Systems (D-66111 Saarbr\u00fccken/D-67663 Kaiserslautern - Germany)","institution_ids":["https://openalex.org/I4210121786"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063753055"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09839682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Volume 20, Issue 2","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":0.9998000264167786,"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":0.9998000264167786,"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":0.9993000030517578,"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/T11567","display_name":"semigroups and automata theory","score":0.9965000152587891,"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/decidability","display_name":"Decidability","score":0.8150361776351929},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6318297386169434},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.5645847916603088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5186747312545776},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.4922288954257965},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.4686274826526642},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4244476556777954},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4140360355377197},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32788580656051636},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.25905001163482666},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25677013397216797},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06204000115394592}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8150361776351929},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6318297386169434},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.5645847916603088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5186747312545776},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.4922288954257965},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.4686274826526642},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4244476556777954},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4140360355377197},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32788580656051636},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.25905001163482666},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25677013397216797},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06204000115394592},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.46298/lmcs-20(2:11)2024","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-20(2:11)2024","pdf_url":"https://lmcs.episciences.org/13724/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04777032v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04777032","pdf_url":"https://hal.science/hal-04777032/document","source":{"id":"https://openalex.org/S4406922466","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":"Logical Methods in Computer Science, 2024, Volume 20, Issue 2, &#x27E8;10.46298/lmcs-20(2:11)2024&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:1c8ef30aaa4a4b82b38348734ea6a73a","is_oa":true,"landing_page_url":"https://doaj.org/article/1c8ef30aaa4a4b82b38348734ea6a73a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 20, Issue 2 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46298/lmcs-20(2:11)2024","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-20(2:11)2024","pdf_url":"https://lmcs.episciences.org/13724/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7400000095367432,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G2402987151","display_name":null,"funder_award_id":"ANR-20-CE","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3032849772","display_name":null,"funder_award_id":"TRR 248","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5437069392","display_name":null,"funder_award_id":"ANR-20-CE25-0012","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7833469426","display_name":null,"funder_award_id":"ANR-20-CE25-001","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G890954746","display_name":null,"funder_award_id":"389792660","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321027","display_name":"Indo-French Centre for the Promotion of Advanced Research","ror":"https://ror.org/017aem598"},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4399360105.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W150877817","https://openalex.org/W1496801598","https://openalex.org/W1561261246","https://openalex.org/W1575647584","https://openalex.org/W1797219784","https://openalex.org/W1864094877","https://openalex.org/W1991813962","https://openalex.org/W2000539732","https://openalex.org/W2006083528","https://openalex.org/W2020183404","https://openalex.org/W2021112905","https://openalex.org/W2093972771","https://openalex.org/W2126544654","https://openalex.org/W2294951539","https://openalex.org/W2773589705","https://openalex.org/W2963754540","https://openalex.org/W2964314311","https://openalex.org/W2991196351","https://openalex.org/W3013335592","https://openalex.org/W3046904175","https://openalex.org/W3195759008","https://openalex.org/W4224983736","https://openalex.org/W4255213956","https://openalex.org/W4282975775","https://openalex.org/W4298290503","https://openalex.org/W4375959527","https://openalex.org/W4394647331"],"related_works":["https://openalex.org/W2323172212","https://openalex.org/W1799780713","https://openalex.org/W2972379433","https://openalex.org/W4323907493","https://openalex.org/W2378613393","https://openalex.org/W2331020993","https://openalex.org/W4383764068","https://openalex.org/W4313551347","https://openalex.org/W1892058059","https://openalex.org/W2951545071"],"abstract_inverted_index":{"The":[0],"Skolem":[1,41,158,185],"problem":[2,7,29,284],"is":[3,78,88,176,242,281,294],"a":[4,13,22,49,141,144,153,213,243,266],"long-standing":[5],"open":[6,46],"in":[8,101,105,108,140,199],"linear":[9,14],"dynamical":[10],"systems:":[11],"can":[12,82,98,133,149],"recurrence":[15],"sequence":[16],"(LRS)":[17],"ever":[18],"reach":[19],"0":[20,129],"from":[21,36,92,136],"given":[23,145,177,295],"initial":[24,38,76,90,138,146],"configuration?":[25],"Similarly,":[26],"the":[27,32,51,75,94,119,157,169,174,181,217,246,252,275,279,283,292],"positivity":[28,188],"asks":[30,210,239],"whether":[31,211,240,262],"LRS":[33,58,95,253],"stays":[34,96],"positive":[35,97],"an":[37,89],"configuration.":[39,147],"Deciding":[40],"(or":[42],"positivity)":[43,160],"has":[44],"been":[45],"for":[47,57,71,204,235,265],"half":[48],"century:":[50],"best":[52],"known":[53],"decidability":[54],"results":[55],"are":[56,69,189,257],"with":[59,224],"special":[60],"properties":[61],"(e.g.,":[62],"low":[63],"order":[64],"recurrences).":[65],"But":[66],"these":[67,165],"problems":[68,115,166,218],"easier":[70],"\"uninitialized\"":[72],"variants,":[73],"where":[74],"configuration":[77,91,139],"not":[79],"fixed":[80],"but":[81],"vary":[83],"arbitrarily:":[84],"checking":[85],"if":[86,128,173,208],"there":[87,241],"which":[93,238,251],"be":[99,134,150,222,288],"decided":[100],"polynomial":[102],"time":[103],"(Tiwari":[104],"2004,":[106],"Braverman":[107],"2006).":[109],"In":[110],"this":[111,270],"paper,":[112],"we":[113,126,263],"consider":[114],"that":[116,164],"lie":[117,167],"between":[118],"initialized":[120],"and":[121,186],"uninitialized":[122],"variants.":[123],"More":[124],"precisely,":[125],"ask":[127,264],"(resp.":[130,159],"negative":[131],"numbers)":[132],"avoided":[135],"every":[137],"neighborhood":[142],"of":[143,156,171,180,248,272],"This":[148],"considered":[151],"as":[152,178,202,296],"robust":[154,184,187],"variant":[155],"problem.":[161],"We":[162],"show":[163],"at":[168],"frontier":[170],"decidability:":[172],"neighbourhood":[175,214,280,293],"part":[179],"input,":[182],"then":[183,216],"Diophantine":[190,200],"hard,":[191],"i.e.,":[192],"solving":[193],"either":[194],"would":[195],"entail":[196],"major":[197],"breakthroughs":[198],"approximations,":[201],"happens":[203],"(non-robust)":[205],"positivity.":[206],"However,":[207],"one":[209],"such":[212],"exists,":[215],"turn":[219],"out":[220,286],"to":[221,232,287],"decidable":[223],"PSPACE":[225],"complexity.":[226],"Our":[227],"techniques":[228],"also":[229],"allow":[230],"us":[231],"tackle":[233],"robustness":[234],"ultimate":[236],"positivity,":[237],"bound":[244,268],"on":[245,261,269],"number":[247,271],"steps":[249],"after":[250],"remains":[254],"positive.":[255],"There":[256],"two":[258],"variants":[259],"depending":[260],"\"uniform\"":[267],"steps.":[273],"For":[274],"non-uniform":[276],"variant,":[277],"when":[278,291],"open,":[282],"turns":[285],"tractable,":[289],"even":[290],"input.":[297]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
