{"id":"https://openalex.org/W2949343847","doi":"https://doi.org/10.1007/978-3-319-63390-9_3","title":"Non-polynomial Worst-Case Analysis of Recursive Programs","display_name":"Non-polynomial Worst-Case Analysis of Recursive Programs","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2949343847","doi":"https://doi.org/10.1007/978-3-319-63390-9_3","mag":"2949343847"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-63390-9_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-63390-9_3","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1705.00317","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052607806","display_name":"Krishnendu Chatterjee","orcid":"https://orcid.org/0000-0002-4561-241X"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Krishnendu Chatterjee","raw_affiliation_strings":["IST Austria, Klosterneuburg, Austria","IST Austria (Institute of Science and Technology Austria) Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IST Austria, Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]},{"raw_affiliation_string":"IST Austria (Institute of Science and Technology Austria) Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031020748","display_name":"Hongfei Fu","orcid":"https://orcid.org/0000-0002-7947-3446"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongfei Fu","raw_affiliation_strings":["State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, People\u2019s Republic of China","Shanghai Jiao Tong University, P. R. China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Shanghai Jiao Tong University, P. R. China#TAB#","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005241421","display_name":"Amir Kafshdar Goharshady","orcid":"https://orcid.org/0000-0003-1702-6584"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Amir Kafshdar Goharshady","raw_affiliation_strings":["IST Austria, Klosterneuburg, Austria","IST Austria, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IST Austria, Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]},{"raw_affiliation_string":"IST Austria, Austria","institution_ids":["https://openalex.org/I157556583"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"4","first_page":"1","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9983999729156494,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9951000213623047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6917119026184082},{"id":"https://openalex.org/keywords/strassen-algorithm","display_name":"Strassen algorithm","score":0.6797044277191162},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.6264879703521729},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.566941499710083},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4759916067123413},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4753822386264801},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4603651762008667},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45791828632354736},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45241260528564453},{"id":"https://openalex.org/keywords/deterministic-algorithm","display_name":"Deterministic algorithm","score":0.43036195635795593},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4114600121974945},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.39073053002357483},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1497788429260254}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6917119026184082},{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.6797044277191162},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.6264879703521729},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.566941499710083},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4759916067123413},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4753822386264801},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4603651762008667},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45791828632354736},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45241260528564453},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.43036195635795593},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4114600121974945},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.39073053002357483},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1497788429260254},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/978-3-319-63390-9_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-63390-9_3","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"doi:10.1145/3339984","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3339984","pdf_url":null,"source":{"id":"https://openalex.org/S41449414","display_name":"ACM Transactions on Programming Languages and Systems","issn_l":"0164-0925","issn":["0164-0925","1558-4593"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Programming Languages and Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1705.00317","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.00317","pdf_url":"https://arxiv.org/pdf/1705.00317","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2949343847","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1705.00317.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:repository.ust.hk:1783.1-107096","is_oa":false,"landing_page_url":"http://lbdiscover.ust.hk/uresolver?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rfr_id=info:sid/HKUST:SPI&rft.genre=article&rft.issn=0164-0925&rft.volume=41&rft.issue=(4)&rft.date=2019&rft.spage=&rft.aulast=Chatterjee&rft.aufirst=&rft.atitle=Non-polynomial+worst-case+analysis+of+recursive+programs&rft.title=ACM+Transactions+on+Programming+Languages+and+Systems","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":"","raw_type":"Article"},{"id":"pmh:oai:repository.ust.hk:1783.1-107143","is_oa":false,"landing_page_url":"http://repository.ust.hk/ir/Record/1783.1-107143","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":"","raw_type":"Conference paper"},{"id":"doi:10.48550/arxiv.1705.00317","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1705.00317","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"pmh:oai:arXiv.org:1705.00317","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.00317","pdf_url":"https://arxiv.org/pdf/1705.00317","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17"}],"awards":[{"id":"https://openalex.org/G2554063606","display_name":"Efficient Algorithms for Computer Aided Verification","funder_award_id":"ICT15-003","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"},{"id":"https://openalex.org/G2655136877","display_name":null,"funder_award_id":"S11407","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G683671635","display_name":null,"funder_award_id":"S11407-N23","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7468986614","display_name":"\u5927\u89c4\u6a21\u6982\u7387\u5e76\u53d1\u5b9e\u65f6\u7cfb\u7edf\u6a21\u578b\u68c0\u9a8c","funder_award_id":"61532019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8986037197","display_name":null,"funder_award_id":"61532019 and 61802254","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321003","display_name":"Vienna Science and Technology Fund","ror":"https://ror.org/01f9mc681"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2949343847.pdf","grobid_xml":"https://content.openalex.org/works/W2949343847.grobid-xml"},"referenced_works_count":76,"referenced_works":["https://openalex.org/W30585784","https://openalex.org/W72346910","https://openalex.org/W94295739","https://openalex.org/W161537417","https://openalex.org/W946815577","https://openalex.org/W1230660382","https://openalex.org/W1481140196","https://openalex.org/W1492171827","https://openalex.org/W1505135855","https://openalex.org/W1523037784","https://openalex.org/W1530375435","https://openalex.org/W1544023751","https://openalex.org/W1551651413","https://openalex.org/W1563352283","https://openalex.org/W1563374593","https://openalex.org/W1568405722","https://openalex.org/W1572346004","https://openalex.org/W1589106570","https://openalex.org/W1589297860","https://openalex.org/W1590648473","https://openalex.org/W1598436734","https://openalex.org/W1599625180","https://openalex.org/W1605543919","https://openalex.org/W1608799719","https://openalex.org/W1636902686","https://openalex.org/W1980177715","https://openalex.org/W1989462119","https://openalex.org/W1993129359","https://openalex.org/W1998724430","https://openalex.org/W2012816689","https://openalex.org/W2037009101","https://openalex.org/W2039205672","https://openalex.org/W2043100293","https://openalex.org/W2055814018","https://openalex.org/W2062306963","https://openalex.org/W2068055184","https://openalex.org/W2073629816","https://openalex.org/W2076285066","https://openalex.org/W2076833152","https://openalex.org/W2109863363","https://openalex.org/W2112969535","https://openalex.org/W2114695797","https://openalex.org/W2120647256","https://openalex.org/W2124909257","https://openalex.org/W2125218864","https://openalex.org/W2135021832","https://openalex.org/W2136333450","https://openalex.org/W2149745672","https://openalex.org/W2166496828","https://openalex.org/W2171496589","https://openalex.org/W2233431969","https://openalex.org/W2258276823","https://openalex.org/W2294463722","https://openalex.org/W2435583538","https://openalex.org/W2461846980","https://openalex.org/W2908549554","https://openalex.org/W2912195676","https://openalex.org/W2912476809","https://openalex.org/W2950486995","https://openalex.org/W2997024788","https://openalex.org/W2998897849","https://openalex.org/W3016662015","https://openalex.org/W3108792179","https://openalex.org/W3141205758","https://openalex.org/W3195620086","https://openalex.org/W3197271110","https://openalex.org/W4232668957","https://openalex.org/W4233310630","https://openalex.org/W4235271643","https://openalex.org/W4239558088","https://openalex.org/W4240185672","https://openalex.org/W4240835555","https://openalex.org/W4251912342","https://openalex.org/W4254838945","https://openalex.org/W6604792996","https://openalex.org/W6827529600"],"related_works":["https://openalex.org/W3141205758","https://openalex.org/W3092390773","https://openalex.org/W60403651","https://openalex.org/W3023091520","https://openalex.org/W2018766465","https://openalex.org/W3027938384","https://openalex.org/W2469269256","https://openalex.org/W2143473941","https://openalex.org/W3037165238","https://openalex.org/W2963056474","https://openalex.org/W2951730160","https://openalex.org/W2964134420","https://openalex.org/W1891288517","https://openalex.org/W2289000419","https://openalex.org/W3101715799","https://openalex.org/W2952763318","https://openalex.org/W2963179814","https://openalex.org/W2786579920","https://openalex.org/W3159345262","https://openalex.org/W2963978854"],"abstract_inverted_index":{"We":[0,42,73,133],"study":[1],"the":[2,65,159,163,210,214,218,246],"problem":[3],"of":[4,12,28,57,67,88,113,147,233],"developing":[5],"efficient":[6],"approaches":[7],"for":[8,22,162,181,187,190,213,238,250],"proving":[9,23],"worst-case":[10,26,55,106,145,175,236],"bounds":[11,27,56,112,146,198,237],"non-deterministic":[13,58],"recursive":[14,59,149],"programs.":[15,30,60],"Ranking":[16],"functions":[17,35,46,69,78],"are":[18],"sound":[19,49],"and":[20,25,50,81,95,122,158,177,184,206,245],"complete":[21,51],"termination":[24],"non-recursive":[29],"First,":[31],"we":[32,168,192,224],"apply":[33],"ranking":[34],"to":[36,53,137,209,220],"recursion,":[37],"resulting":[38],"in":[39,70],"measure":[40,45,68,77],"functions.":[41],"show":[43,74,226],"that":[44,75,139,200,227],"provide":[47],"a":[48],"approach":[52,109,141,229],"prove":[54],"Our":[61],"second":[62],"contribution":[63],"is":[64,129,202,207,230],"synthesis":[66],"non-polynomial":[71,76,222],"forms.":[72],"with":[79],"logarithm":[80],"exponentiation":[82,91],"can":[83,110,142],"be":[84],"synthesized":[85],"through":[86],"abstraction":[87],"logarithmic":[89],"or":[90],"terms,":[92],"Farkas":[93],"Lemma,":[94],"Handelman\u2019s":[96],"Theorem":[97],"using":[98],"linear":[99],"programming.":[100],"While":[101],"previous":[102],"methods":[103],"obtain":[104,144,169,193],"polynomial":[105,182,235],"bounds,":[107,223],"our":[108,140,228],"synthesize":[111,221],"various":[114],"forms":[115],"including":[116],"O(":[117,123,170,194],"n":[118,120,124,171,173,195],"log":[119,172],")":[121,174,197],"r":[125,128,196,201],"),":[126],"where":[127,167],"not":[130,203],"an":[131,204],"integer.":[132],"present":[134],"experimental":[135],"results":[136],"demonstrate":[138],"efficiently":[143],"classical":[148,239],"algorithms":[150],"such":[151,199,241],"as":[152,242],"(i)":[153],"Merge":[154],"sort,":[155,157],"Heap":[156],"divide-and-conquer":[160],"algorithm":[161,180,186,249],"Closest":[164],"Pair":[165],"problem,":[166],"bound,":[176],"(ii)":[178],"Karatsuba\u2019s":[179],"multiplication":[183],"Strassen\u2019s":[185],"matrix":[188],"multiplication,":[189],"which":[191],"integer":[205],"close":[208],"best-known":[211],"bound":[212],"respective":[215],"algorithm.":[216],"Besides":[217],"ability":[219],"also":[225],"equally":[231],"capable":[232],"obtaining":[234],"programs":[240],"Quick":[243],"sort":[244],"dynamic":[247],"programming":[248],"computing":[251],"Fibonacci":[252],"numbers.":[253]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}