{"id":"https://openalex.org/W4400166098","doi":"https://doi.org/10.1007/978-3-031-63498-7_21","title":"Satisfiability Modulo Exponential Integer Arithmetic","display_name":"Satisfiability Modulo Exponential Integer Arithmetic","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4400166098","doi":"https://doi.org/10.1007/978-3-031-63498-7_21"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-63498-7_21","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-63498-7_21","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-63498-7_21.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/10.1007/978-3-031-63498-7_21.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087390223","display_name":"Florian Frohn","orcid":"https://orcid.org/0000-0003-0902-1994"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florian Frohn","raw_affiliation_strings":["RWTH Aachen University, Aachen, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0902-1994","affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025232172","display_name":"J\u00fcrgen Giesl","orcid":"https://orcid.org/0000-0003-0283-8520"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"J\u00fcrgen Giesl","raw_affiliation_strings":["RWTH Aachen University, Aachen, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0283-8520","affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025232172"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":2.7884,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.88767583,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"344","last_page":"365"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":1.0,"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":1.0,"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":0.9995999932289124,"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/integer","display_name":"Integer (computer science)","score":0.5664874315261841},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.565329909324646},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.5093632936477661},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5023746490478516},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.501558780670166},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.48855409026145935},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4871211051940918},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4744613766670227},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4699842035770416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4527251720428467},{"id":"https://openalex.org/keywords/satisfiability-modulo-theories","display_name":"Satisfiability modulo theories","score":0.4416447877883911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4374796450138092},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3597790002822876},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3252471685409546},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.0921524167060852},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07912570238113403}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5664874315261841},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.565329909324646},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.5093632936477661},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5023746490478516},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.501558780670166},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.48855409026145935},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4871211051940918},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4744613766670227},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4699842035770416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4527251720428467},{"id":"https://openalex.org/C164155591","wikidata":"https://www.wikidata.org/wiki/Q2067766","display_name":"Satisfiability modulo theories","level":2,"score":0.4416447877883911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4374796450138092},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3597790002822876},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3252471685409546},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0921524167060852},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07912570238113403},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-63498-7_21","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-63498-7_21","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-63498-7_21.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"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-63498-7_21","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-63498-7_21","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-63498-7_21.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":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400166098.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W221832247","https://openalex.org/W333834217","https://openalex.org/W1480909796","https://openalex.org/W1496681274","https://openalex.org/W1519551513","https://openalex.org/W1540580590","https://openalex.org/W1977456312","https://openalex.org/W2008288068","https://openalex.org/W2031276295","https://openalex.org/W2095810701","https://openalex.org/W2158395308","https://openalex.org/W2163850966","https://openalex.org/W2809752556","https://openalex.org/W2889414920","https://openalex.org/W2935588095","https://openalex.org/W2957046311","https://openalex.org/W2985800447","https://openalex.org/W3100830552","https://openalex.org/W3164356218","https://openalex.org/W4225922019","https://openalex.org/W4289104025","https://openalex.org/W4312267877","https://openalex.org/W4372283943","https://openalex.org/W4379165432","https://openalex.org/W4386363935","https://openalex.org/W4387885360","https://openalex.org/W4389312394","https://openalex.org/W4391556310","https://openalex.org/W4400166098"],"related_works":["https://openalex.org/W2532989613","https://openalex.org/W2122450783","https://openalex.org/W4301409452","https://openalex.org/W2578463151","https://openalex.org/W2810367355","https://openalex.org/W2275420537","https://openalex.org/W1483783534","https://openalex.org/W4379142300","https://openalex.org/W4302330337","https://openalex.org/W4386723279"],"abstract_inverted_index":{"Abstract":[0],"SMT":[1],"solvers":[2],"use":[3],"sophisticated":[4],"techniques":[5],"for":[6],"polynomial":[7,73],"(linear":[8],"or":[9],"non-linear)":[10],"integer":[11,16,74],"arithmetic.":[12],"In":[13,47],"contrast,":[14],"non-polynomial":[15],"arithmetic":[17,61,75],"has":[18,53],"mostly":[19],"been":[20,54],"neglected":[21],"so":[22],"far.":[23],"However,":[24],"in":[25,117],"the":[26,37,40,48,80,90,94,100],"context":[27],"of":[28,39,72,102,107],"program":[29],"verification,":[30],"polynomials":[31],"are":[32],"often":[33],"insufficient":[34],"to":[35,45,57,69,84],"capture":[36],"behavior":[38],"analyzed":[41],"system":[42],"without":[43],"resorting":[44],"approximations.":[46],"last":[49],"years,":[50],"incremental":[51],"linearization":[52],"applied":[55],"successfully":[56],"satisfiability":[58],"modulo":[59],"real":[60],"with":[62,76],"transcendental":[63],"functions.":[64,78],"We":[65],"adapt":[66],"this":[67],"approach":[68,113],"an":[70],"extension":[71],"exponential":[77],"Here,":[79],"key":[81],"challenge":[82],"is":[83,114],"compute":[85],"suitable":[86],"lemmas":[87],"that":[88,111],"eliminate":[89],"current":[91],"model":[92],"from":[93],"search":[95],"space":[96],"if":[97],"it":[98],"violates":[99],"semantics":[101],"exponentiation.":[103],"An":[104],"empirical":[105],"evaluation":[106],"our":[108,112],"implementation":[109],"shows":[110],"highly":[115],"effective":[116],"practice.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
