{"id":"https://openalex.org/W4410043368","doi":"https://doi.org/10.1007/978-3-031-91121-7_1","title":"Efficient Synthesis of Tight Polynomial Upper-Bounds for Systems of Conditional Polynomial Recurrences","display_name":"Efficient Synthesis of Tight Polynomial Upper-Bounds for Systems of Conditional Polynomial Recurrences","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4410043368","doi":"https://doi.org/10.1007/978-3-031-91121-7_1"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-91121-7_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-91121-7_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-91121-7_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-91121-7_1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007636554","display_name":"Amir K. Goharshady","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Amir K. Goharshady","raw_affiliation_strings":["University of Oxford, Oxford, UK"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013054213","display_name":"S. Hitarth","orcid":null},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"S. Hitarth","raw_affiliation_strings":["Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020870701","display_name":"Sergei Novozhilov","orcid":"https://orcid.org/0009-0001-5934-0806"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Sergei Novozhilov","raw_affiliation_strings":["Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007636554"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26759062,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9991000294685364,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9979000091552734,"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/computer-science","display_name":"Computer science","score":0.7153232097625732},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.631128191947937},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4096720814704895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24963513016700745}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7153232097625732},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.631128191947937},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4096720814704895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24963513016700745},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-031-91121-7_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-91121-7_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-91121-7_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-148416","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-148416","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Conference paper"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-91121-7_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-91121-7_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-91121-7_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320329018","display_name":"Ethereum Foundation","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410043368.pdf","grobid_xml":"https://content.openalex.org/works/W4410043368.grobid-xml"},"referenced_works_count":83,"referenced_works":["https://openalex.org/W1781094","https://openalex.org/W30585784","https://openalex.org/W87140126","https://openalex.org/W94295739","https://openalex.org/W136633354","https://openalex.org/W653291882","https://openalex.org/W1230660382","https://openalex.org/W1480909796","https://openalex.org/W1530375435","https://openalex.org/W1544023751","https://openalex.org/W1563352283","https://openalex.org/W1563374593","https://openalex.org/W1585981132","https://openalex.org/W1598436734","https://openalex.org/W1821417028","https://openalex.org/W1963833875","https://openalex.org/W1973393028","https://openalex.org/W1993388844","https://openalex.org/W2035476608","https://openalex.org/W2037009101","https://openalex.org/W2058033966","https://openalex.org/W2067754486","https://openalex.org/W2069852500","https://openalex.org/W2073629816","https://openalex.org/W2089718638","https://openalex.org/W2116087731","https://openalex.org/W2119912580","https://openalex.org/W2139929430","https://openalex.org/W2194223632","https://openalex.org/W2233431969","https://openalex.org/W2264437737","https://openalex.org/W2289508293","https://openalex.org/W2398327122","https://openalex.org/W2408512871","https://openalex.org/W2435583538","https://openalex.org/W2569392808","https://openalex.org/W2612425693","https://openalex.org/W2625924363","https://openalex.org/W2735409225","https://openalex.org/W2757243080","https://openalex.org/W2809851475","https://openalex.org/W2880875791","https://openalex.org/W2914414140","https://openalex.org/W2914740438","https://openalex.org/W2963296553","https://openalex.org/W2963595697","https://openalex.org/W2979551317","https://openalex.org/W2980978064","https://openalex.org/W2982014993","https://openalex.org/W2989189770","https://openalex.org/W2997024788","https://openalex.org/W3009691493","https://openalex.org/W3033229382","https://openalex.org/W3033865919","https://openalex.org/W3046984529","https://openalex.org/W3118657565","https://openalex.org/W3141205758","https://openalex.org/W3166047986","https://openalex.org/W3176250057","https://openalex.org/W3185017891","https://openalex.org/W3191748134","https://openalex.org/W3205892009","https://openalex.org/W4220906786","https://openalex.org/W4225922019","https://openalex.org/W4237541087","https://openalex.org/W4241936027","https://openalex.org/W4246575101","https://openalex.org/W4246691913","https://openalex.org/W4255442211","https://openalex.org/W4281612951","https://openalex.org/W4283462359","https://openalex.org/W4362659488","https://openalex.org/W4362659518","https://openalex.org/W4366449580","https://openalex.org/W4384471480","https://openalex.org/W4387673899","https://openalex.org/W4387687567","https://openalex.org/W4390603443","https://openalex.org/W4392577507","https://openalex.org/W4397288754","https://openalex.org/W4402425134","https://openalex.org/W4402425289","https://openalex.org/W6911980827"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"Abstract":[0],"Recurrence":[1,157],"relations":[2],"are":[3],"used":[4],"in":[5,171],"a":[6,65,78,149,188,213],"wide":[7,150],"variety":[8],"of":[9,29,64,81,84,95,104,111,114,128,152,168,202,231,254],"static":[10],"program":[11],"analysis":[12],"tasks":[13],"such":[14,47,105],"as":[15,48,261],"loop":[16],"summarization,":[17],"invariant":[18],"generation,":[19],"and,":[20],"most":[21],"classically,":[22],"modeling":[23],"the":[24,39,49,55,85,102,112,115,182,200,203,229],"(asymptotic)":[25],"worst-case":[26],"runtime":[27],"behavior":[28,134],"recursive":[30,133],"divide-and-conquer":[31],"algorithms.":[32],"In":[33,140],"this":[34,45,141],"work,":[35,142],"we":[36,143],"focus":[37],"on":[38,197,199],"latter":[40],"use-case.":[41],"Classical":[42],"methods":[43,120,217],"for":[44,212,252],"problem,":[46],"well-known":[50],"Master":[51],"Theorem":[52],"(MT)":[53],"or":[54,137,236],"Akra-Bazzi":[56],"method":[57,245],"(AB)":[58],"can":[59,121,175,192],"only":[60],"handle":[61,122],"single":[62,189],"recurrences":[63,125,129,153,170],"certain":[66],"limited":[67,186],"form.":[68],"Specifically,":[69],"MT":[70,91],"requires":[71,100],"that":[72,101,130],"each":[73],"instance":[74,174],"be":[75,107,176],"divided":[76,177],"into":[77,178],"fixed":[79,108,256],"number":[80,103],"smaller":[82],"sub-instances":[83,94,106],"same":[86],"size":[87,113],".":[88],"AB":[89],"generalizes":[90],"by":[92],"allowing":[93],"different":[96],"sizes,":[97],"but":[98],"still":[99],"and":[109,147,165,191,218,223,248,258],"independent":[110],"original":[116],"instance.":[117],"Moreover,":[118,181],"these":[119,145],"neither":[123],"multi-variate":[124,169],"nor":[126],"systems":[127,167],"model":[131],"non-simple":[132],"among":[135],"two":[136],"more":[138],"procedures.":[139],"lift":[144],"restrictions":[146],"consider":[148],"family":[151],"called":[154],"Generalized":[155],"Polynomial":[156],"Systems":[158],"(GPRS).":[159],"Our":[160,226],"setting":[161],"is":[162,184,246],"highly":[163],"expressive":[164],"allows":[166],"which":[172],"an":[173],"polynomially-many":[179],"sub-instances.":[180],"division":[183],"not":[185],"to":[187,208,234,263],"rule":[190],"have":[193],"several":[194],"cases":[195],"based":[196],"conditions":[198],"values":[201],"variables.":[204],"We":[205],"show":[206],"how":[207],"obtain":[209],"polynomial":[210,232],"upper-bounds":[211,233],"GPRS":[214],"using":[215],"template-based":[216],"classical":[219],"theorems":[220],"from":[221],"polyhedral":[222],"algebraic":[224],"geometry.":[225],"approach":[227],"reduces":[228],"synthesis":[230],"linear":[235],"semi-definite":[237],"programming":[238],"instances,":[239],"enabling":[240],"efficient":[241],"solutions.":[242],"Crucially,":[243],"our":[244],"sound":[247],"semi-complete,":[249],"i.e.":[250],"complete":[251],"polynomials":[253],"any":[255],"degree":[257],"obtains":[259],"concrete,":[260],"opposed":[262],"asymptotic,":[264],"upper-bounds.":[265]},"counts_by_year":[],"updated_date":"2026-03-26T15:22:09.906841","created_date":"2025-10-10T00:00:00"}
