{"id":"https://openalex.org/W4233428758","doi":"https://doi.org/10.1109/date.2004.1268875","title":"Refinement of mixed-signals systems with affine arithmetic","display_name":"Refinement of mixed-signals systems with affine arithmetic","publication_year":2004,"publication_date":"2004-06-21","ids":{"openalex":"https://openalex.org/W4233428758","doi":"https://doi.org/10.1109/date.2004.1268875"},"language":"en","primary_location":{"id":"doi:10.1109/date.2004.1268875","is_oa":false,"landing_page_url":"https://doi.org/10.1109/date.2004.1268875","pdf_url":null,"source":{"id":"https://openalex.org/S4363608792","display_name":"Proceedings Design, Automation and Test in Europe Conference and Exhibition","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings Design, Automation and Test in Europe Conference and Exhibition","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103027575","display_name":"Christoph Grimm","orcid":"https://orcid.org/0000-0002-5930-7563"},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]},{"id":"https://openalex.org/I5237613","display_name":"Frankfurt University of Applied Sciences","ror":"https://ror.org/02r625m11","country_code":"DE","type":"education","lineage":["https://openalex.org/I5237613"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ch. Grimm","raw_affiliation_strings":["Professur Technische Informatik, University of Frankfurt am Main, Frankfurt, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Professur Technische Informatik, University of Frankfurt am Main, Frankfurt, Germany","institution_ids":["https://openalex.org/I114090438","https://openalex.org/I5237613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025204970","display_name":"W. Heupke","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]},{"id":"https://openalex.org/I5237613","display_name":"Frankfurt University of Applied Sciences","ror":"https://ror.org/02r625m11","country_code":"DE","type":"education","lineage":["https://openalex.org/I5237613"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"W. Heupke","raw_affiliation_strings":["Professur Technische Informatik, University of Frankfurt am Main, Frankfurt, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Professur Technische Informatik, University of Frankfurt am Main, Frankfurt, Germany","institution_ids":["https://openalex.org/I114090438","https://openalex.org/I5237613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057980771","display_name":"Klaus Waldschmidt","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]},{"id":"https://openalex.org/I5237613","display_name":"Frankfurt University of Applied Sciences","ror":"https://ror.org/02r625m11","country_code":"DE","type":"education","lineage":["https://openalex.org/I5237613"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"K. Waldschmidt","raw_affiliation_strings":["Professur Technische Informatik, University of Frankfurt am Main, Frankfurt, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Professur Technische Informatik, University of Frankfurt am Main, Frankfurt, Germany","institution_ids":["https://openalex.org/I114090438","https://openalex.org/I5237613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"372","last_page":"377"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9987999796867371,"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":0.9987999796867371,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9987999796867371,"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/T10323","display_name":"Analog and Mixed-Signal Circuit Design","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/affine-arithmetic","display_name":"Affine arithmetic","score":0.9170715808868408},{"id":"https://openalex.org/keywords/executable","display_name":"Executable","score":0.8680128455162048},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6996866464614868},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6918978095054626},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.6084936261177063},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5417140126228333},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5119506120681763},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.46356189250946045},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45914411544799805},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4430195689201355},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.42988717555999756},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.41060304641723633},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.32649558782577515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23226335644721985},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.11126014590263367}],"concepts":[{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.9170715808868408},{"id":"https://openalex.org/C160145156","wikidata":"https://www.wikidata.org/wiki/Q778586","display_name":"Executable","level":2,"score":0.8680128455162048},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6996866464614868},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6918978095054626},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.6084936261177063},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5417140126228333},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5119506120681763},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.46356189250946045},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45914411544799805},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4430195689201355},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.42988717555999756},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.41060304641723633},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.32649558782577515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23226335644721985},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.11126014590263367},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/date.2004.1268875","is_oa":false,"landing_page_url":"https://doi.org/10.1109/date.2004.1268875","pdf_url":null,"source":{"id":"https://openalex.org/S4363608792","display_name":"Proceedings Design, Automation and Test in Europe Conference and Exhibition","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings Design, Automation and Test in Europe Conference and Exhibition","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W53399449","https://openalex.org/W73680957","https://openalex.org/W1483379332","https://openalex.org/W2137808030","https://openalex.org/W2148734712","https://openalex.org/W2746733541","https://openalex.org/W4235638977","https://openalex.org/W4239229050","https://openalex.org/W6602939453","https://openalex.org/W6742985877"],"related_works":["https://openalex.org/W3129089851","https://openalex.org/W2147412345","https://openalex.org/W1531645310","https://openalex.org/W2568181300","https://openalex.org/W2118036253","https://openalex.org/W1559551218","https://openalex.org/W2752272446","https://openalex.org/W4235638977","https://openalex.org/W4254410407","https://openalex.org/W2161871086"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"a":[3],"framework":[4,45],"for":[5],"the":[6,36,49],"refinement":[7],"of":[8,29,42,51],"control":[9],"and":[10,21,34,47],"signal":[11],"processing":[12],"functions.":[13],"The":[14,44],"design":[15],"starts":[16],"with":[17,39],"an":[18],"executable":[19],"specification,":[20],"allowed":[22],"deviations":[23],"thereof.":[24],"Refinement":[25],"steps":[26],"introduce":[27],"models":[28],"analog":[30],"or":[31],"digital":[32],"implementations,":[33],"augment":[35],"'ideal'":[37],"behavior":[38],"different":[40],"sources":[41],"uncertainty.":[43],"verifies":[46],"analyzes":[48],"influence":[50],"these":[52],"uncertainties":[53],"on":[54],"system":[55],"properties":[56],"using":[57],"affine":[58],"arithmetic.":[59]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}