{"id":"https://openalex.org/W4253715966","doi":"https://doi.org/10.1109/fmcad.2016.7886676","title":"Equivalence checking using Gr\u00f6bner bases","display_name":"Equivalence checking using Gr\u00f6bner bases","publication_year":2016,"publication_date":"2016-10-01","ids":{"openalex":"https://openalex.org/W4253715966","doi":"https://doi.org/10.1109/fmcad.2016.7886676"},"language":"en","primary_location":{"id":"doi:10.1109/fmcad.2016.7886676","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fmcad.2016.7886676","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 Formal Methods in Computer-Aided Design (FMCAD)","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/A5069061017","display_name":"Amr Sayed-Ahmed","orcid":null},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Amr Sayed-Ahmed","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, University of Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111976990","display_name":"Daniel GroBe","orcid":null},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Daniel Grobe","raw_affiliation_strings":["DFKI GmbH, Cyber-Physical Systems, Bremen, Germany","Faculty of Mathematics and Computer Science, University of Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DFKI GmbH, Cyber-Physical Systems, Bremen, Germany","institution_ids":[]},{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084007478","display_name":"Mathias Soeken","orcid":"https://orcid.org/0000-0002-0229-8766"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Mathias Soeken","raw_affiliation_strings":["EPFL, Integrated Systems Laboratory (LSI), Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EPFL, Integrated Systems Laboratory (LSI), Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071742136","display_name":"Rolf Drechsler","orcid":"https://orcid.org/0000-0002-9872-1740"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rolf Drechsler","raw_affiliation_strings":["DFKI GmbH, Cyber-Physical Systems, Bremen, Germany","Faculty of Mathematics and Computer Science, University of Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DFKI GmbH, Cyber-Physical Systems, Bremen, Germany","institution_ids":[]},{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"169","last_page":"176"},"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/T10951","display_name":"Cryptographic Implementations and Security","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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9939000010490417,"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/formal-equivalence-checking","display_name":"Formal equivalence checking","score":0.6974555850028992},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.5680290460586548},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5650725960731506},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5580014586448669},{"id":"https://openalex.org/keywords/logical-equivalence","display_name":"Logical equivalence","score":0.5500579476356506},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.543703556060791},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.5264861583709717},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5208088159561157},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.5041974782943726},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.47270676493644714},{"id":"https://openalex.org/keywords/combinational-logic","display_name":"Combinational logic","score":0.42666754126548767},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42152440547943115},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4206121563911438},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3761720657348633},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37285614013671875},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.36865025758743286},{"id":"https://openalex.org/keywords/logic-gate","display_name":"Logic gate","score":0.26480093598365784},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.20581495761871338}],"concepts":[{"id":"https://openalex.org/C96654402","wikidata":"https://www.wikidata.org/wiki/Q5469962","display_name":"Formal equivalence checking","level":3,"score":0.6974555850028992},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5680290460586548},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5650725960731506},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5580014586448669},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.5500579476356506},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.543703556060791},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.5264861583709717},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5208088159561157},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.5041974782943726},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.47270676493644714},{"id":"https://openalex.org/C81409106","wikidata":"https://www.wikidata.org/wiki/Q76505","display_name":"Combinational logic","level":3,"score":0.42666754126548767},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42152440547943115},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4206121563911438},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3761720657348633},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37285614013671875},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.36865025758743286},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.26480093598365784},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.20581495761871338},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fmcad.2016.7886676","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fmcad.2016.7886676","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 Formal Methods in Computer-Aided Design (FMCAD)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W34381828","https://openalex.org/W1528837436","https://openalex.org/W1939160307","https://openalex.org/W2000519336","https://openalex.org/W2075497274","https://openalex.org/W2104779491","https://openalex.org/W2140132043","https://openalex.org/W2282171944","https://openalex.org/W2344855325","https://openalex.org/W2370798236","https://openalex.org/W2511380445","https://openalex.org/W2515967056","https://openalex.org/W3151473321","https://openalex.org/W4236423066","https://openalex.org/W4250501683","https://openalex.org/W6631725144","https://openalex.org/W6665802101"],"related_works":["https://openalex.org/W2363848182","https://openalex.org/W2115941521","https://openalex.org/W2366877601","https://openalex.org/W2728756936","https://openalex.org/W4379403008","https://openalex.org/W2121954536","https://openalex.org/W159155636","https://openalex.org/W4395017379","https://openalex.org/W309498622","https://openalex.org/W2603868029"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,6,60,85,89,97,101,108,133,147,153],"recent":[3],"success":[4],"of":[5,13,51,66,88,149,155],"algebraic":[7,22,75],"computation":[8],"technique":[9],"in":[10,64,96],"formal":[11],"verification":[12],"large":[14],"and":[15,69,80,92,119,138,168],"optimized":[16,167],"gate-level":[17],"multipliers,":[18],"this":[19],"paper":[20],"proposes":[21],"equivalence":[23,154],"checking":[24,152],"for":[25,44,107,151],"handling":[26],"circuits":[27,40,63,91],"that":[28],"contain":[29],"both":[30,143],"complex":[31],"arithmetic":[32,117,129],"components":[33,118,135],"as":[34,36],"well":[35],"control":[37],"logic.":[38],"These":[39],"pose":[41],"major":[42],"challenges":[43],"existing":[45],"proof":[46],"techniques.":[47],"The":[48],"basic":[49],"idea":[50],"Algebraic":[52],"Combinational":[53],"Equivalence":[54],"Checking":[55],"(ACEC)":[56],"is":[57],"to":[58,115,120,123,136],"model":[59],"two":[61,90],"compared":[62],"form":[65],"Gr\u00f6bner":[67],"bases":[68],"combine":[70],"them":[71,122],"into":[72],"a":[73,156],"single":[74],"model.":[76,99],"It":[77],"generates":[78],"bit":[79],"word":[81],"relationship":[82],"candidates":[83],"between":[84,142],"internal":[86,140],"variables":[87],"tests":[93],"their":[94],"membership":[95,102],"combined":[98],"Since":[100],"testing":[103],"does":[104],"not":[105],"scale":[106],"described":[109],"setting,":[110],"we":[111,127],"propose":[112,128],"reverse":[113],"engineering":[114],"extract":[116],"abstract":[121],"canonical":[124],"representations.":[125],"Further":[126],"sweeping":[130],"which":[131],"utilizes":[132],"abstracted":[134],"find":[137],"prove":[139],"equivalences":[141],"circuits.":[144],"We":[145],"demonstrate":[146],"applicability":[148],"ACEC":[150],"floating":[157],"point":[158],"multiplier":[159],"(including":[160],"full":[161],"IEEE-754":[162],"rounding":[163],"scheme)":[164],"against":[165],"several":[166],"diversified":[169],"implementations.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-07-27T08:26:11.824852","created_date":"2025-10-10T00:00:00"}
