{"id":"https://openalex.org/W2144735470","doi":"https://doi.org/10.1145/2206781.2206859","title":"Extending symmetric variable-pair transitivities using state-space transformations","display_name":"Extending symmetric variable-pair transitivities using state-space transformations","publication_year":2012,"publication_date":"2012-05-03","ids":{"openalex":"https://openalex.org/W2144735470","doi":"https://doi.org/10.1145/2206781.2206859","mag":"2144735470"},"language":"en","primary_location":{"id":"doi:10.1145/2206781.2206859","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2206781.2206859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the great lakes symposium on VLSI","raw_type":"proceedings-article"},"type":"article","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/A5064063616","display_name":"Peter M. Maurer","orcid":"https://orcid.org/0000-0002-7194-2981"},"institutions":[{"id":"https://openalex.org/I157394403","display_name":"Baylor University","ror":"https://ror.org/005781934","country_code":"US","type":"education","lineage":["https://openalex.org/I157394403"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peter M. Maurer","raw_affiliation_strings":["Baylor University, Waco, TX, USA","Baylor University, Waco, TX USA"],"affiliations":[{"raw_affiliation_string":"Baylor University, Waco, TX, USA","institution_ids":["https://openalex.org/I157394403"]},{"raw_affiliation_string":"Baylor University, Waco, TX USA","institution_ids":["https://openalex.org/I157394403"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064063616"],"corresponding_institution_ids":["https://openalex.org/I157394403"],"apc_list":null,"apc_paid":null,"fwci":0.337,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63883671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"315","last_page":"320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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":0.9998999834060669,"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/T11005","display_name":"Radiation Effects in Electronics","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9975000023841858,"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/homogeneous-space","display_name":"Homogeneous space","score":0.8753494024276733},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.6247586607933044},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.600593090057373},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5508626699447632},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.5292094349861145},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4795615077018738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4716692864894867},{"id":"https://openalex.org/keywords/boolean-data-type","display_name":"Boolean data type","score":0.46199941635131836},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4504963159561157},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4397459328174591},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41689956188201904},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3674243092536926},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3009602129459381},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1646440625190735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12562212347984314}],"concepts":[{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.8753494024276733},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.6247586607933044},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.600593090057373},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5508626699447632},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.5292094349861145},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4795615077018738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4716692864894867},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.46199941635131836},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4504963159561157},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4397459328174591},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41689956188201904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3674243092536926},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3009602129459381},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1646440625190735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12562212347984314},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2206781.2206859","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2206781.2206859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the great lakes symposium on VLSI","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":25,"referenced_works":["https://openalex.org/W101369028","https://openalex.org/W1518237063","https://openalex.org/W1522712853","https://openalex.org/W1633302286","https://openalex.org/W1674524317","https://openalex.org/W1974711669","https://openalex.org/W2058381227","https://openalex.org/W2068422506","https://openalex.org/W2102128707","https://openalex.org/W2103240723","https://openalex.org/W2106668637","https://openalex.org/W2111368429","https://openalex.org/W2122479308","https://openalex.org/W2144869414","https://openalex.org/W2152056125","https://openalex.org/W2153780507","https://openalex.org/W2168679029","https://openalex.org/W2292378071","https://openalex.org/W2913483809","https://openalex.org/W3151969339","https://openalex.org/W4234499477","https://openalex.org/W4299701014","https://openalex.org/W6604226374","https://openalex.org/W6637282363","https://openalex.org/W6682123326"],"related_works":["https://openalex.org/W2092886012","https://openalex.org/W2170281757","https://openalex.org/W2145874891","https://openalex.org/W2119028753","https://openalex.org/W2790802381","https://openalex.org/W2163637248","https://openalex.org/W1982026196","https://openalex.org/W3094037537","https://openalex.org/W2511750106","https://openalex.org/W2008298629"],"abstract_inverted_index":{"Detecting":[0],"the":[1,14,35,72],"symmetries":[2,54],"of":[3,21,37,62,88],"a":[4,38],"Boolean":[5],"function":[6,39],"can":[7],"lead":[8],"to":[9,33,41,48,70,81,84],"simpler":[10],"implementations":[11],"both":[12],"at":[13],"hardware":[15],"and":[16],"software":[17],"level.":[18],"Large":[19],"clusters":[20,87],"mutually":[22],"symmetric":[23,50,89],"variables":[24],"are":[25,55,64],"more":[26,59,73],"advantageous":[27],"than":[28,92],"small":[29],"clusters.":[30],"One":[31],"way":[32],"extend":[34],"symmetry":[36],"is":[40],"detect":[42],"abstract":[43],"two-cofactor":[44],"relations":[45,63,75],"in":[46],"addition":[47],"ordinary":[49,53,77,97],"relations.":[51],"Unfortunately,":[52],"simply":[56],"transitive":[57],"but":[58],"complex":[60,74],"types":[61],"not.":[65],"This":[66],"paper":[67],"shows":[68],"how":[69],"convert":[71],"into":[76],"symmetries,":[78],"allowing":[79],"them":[80],"be":[82,94],"used":[83],"form":[85],"large":[86],"variables,":[90],"larger":[91],"would":[93],"possible":[95],"using":[96],"symmetries.":[98]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
