{"id":"https://openalex.org/W2101101130","doi":"https://doi.org/10.1145/1146909.1147044","title":"Symmetry detection for large Boolean functions using circuit representation, simulation, and satisfiability","display_name":"Symmetry detection for large Boolean functions using circuit representation, simulation, and satisfiability","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2101101130","doi":"https://doi.org/10.1145/1146909.1147044","mag":"2101101130"},"language":"en","primary_location":{"id":"doi:10.1145/1146909.1147044","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1146909.1147044","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 43rd annual conference on Design automation - DAC '06","raw_type":"proceedings-article"},"type":"conference-abstract","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/A5038455726","display_name":"Jin S. Zhang","orcid":"https://orcid.org/0000-0002-1936-7780"},"institutions":[{"id":"https://openalex.org/I126345244","display_name":"Portland State University","ror":"https://ror.org/00yn2fy02","country_code":"US","type":"education","lineage":["https://openalex.org/I126345244"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jin S. Zhang","raw_affiliation_strings":["Portland State University, Portland, OR","Dept. of Electr. & Comput. Eng., Portland State Univ., OR#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Portland State University, Portland, OR","institution_ids":["https://openalex.org/I126345244"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Portland State Univ., OR#TAB#","institution_ids":["https://openalex.org/I126345244"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110450560","display_name":"Alan Mishchenko","orcid":"https://orcid.org/0009-0004-1303-6261"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan Mishchenko","raw_affiliation_strings":["University of California at Berkeley, Berkeley, CA","University of California at Berkeley Berkeley CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California at Berkeley, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California at Berkeley Berkeley CA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064568178","display_name":"Robert K. Brayton","orcid":"https://orcid.org/0000-0002-3861-1718"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert Brayton","raw_affiliation_strings":["University of California at Berkeley, Berkeley, CA","University of California at Berkeley Berkeley CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California at Berkeley, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California at Berkeley Berkeley CA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040622659","display_name":"Malgorzata Chrzanowska-Jeske","orcid":"https://orcid.org/0000-0001-5927-1751"},"institutions":[{"id":"https://openalex.org/I126345244","display_name":"Portland State University","ror":"https://ror.org/00yn2fy02","country_code":"US","type":"education","lineage":["https://openalex.org/I126345244"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Malgorzata Chrzanowska-Jeske","raw_affiliation_strings":["Portland State University, Portland, OR","[Portland State University Portland, OR]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Portland State University, Portland, OR","institution_ids":["https://openalex.org/I126345244"]},{"raw_affiliation_string":"[Portland State University Portland, OR]","institution_ids":["https://openalex.org/I126345244"]}]}],"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":24,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"510","last_page":"510"},"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.805843710899353},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.762119710445404},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.6308563947677612},{"id":"https://openalex.org/keywords/and-inverter-graph","display_name":"And-inverter graph","score":0.6201054453849792},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6031240224838257},{"id":"https://openalex.org/keywords/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.5354148745536804},{"id":"https://openalex.org/keywords/true-quantified-boolean-formula","display_name":"True quantified Boolean formula","score":0.5284179449081421},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.527549684047699},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4946865737438202},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.48946917057037354},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.47658368945121765},{"id":"https://openalex.org/keywords/product-term","display_name":"Product term","score":0.45090076327323914},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4469777047634125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26027119159698486},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.1555723249912262},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.12514597177505493}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.805843710899353},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.762119710445404},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.6308563947677612},{"id":"https://openalex.org/C196836630","wikidata":"https://www.wikidata.org/wiki/Q4753279","display_name":"And-inverter graph","level":4,"score":0.6201054453849792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6031240224838257},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.5354148745536804},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.5284179449081421},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.527549684047699},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4946865737438202},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.48946917057037354},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.47658368945121765},{"id":"https://openalex.org/C9429942","wikidata":"https://www.wikidata.org/wiki/Q1781698","display_name":"Product term","level":5,"score":0.45090076327323914},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4469777047634125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26027119159698486},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.1555723249912262},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.12514597177505493},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"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/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1146909.1147044","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1146909.1147044","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 43rd annual conference on Design automation - DAC '06","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.3159","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.3159","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.berkeley.edu/~alanmi/publications/2006/dac06_sym.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.85.9030","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.9030","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.dac.com/data2/43rd/43acceptedpapers.nsf/0c4c09c6ffa905c487256b7b007afb72/c8604e0716a1543a8725715500745264/$FILE/32_1.PDF","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.93.2410","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.2410","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.berkeley.edu/~brayton/publications/2006/dac06_sym.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W35668030","https://openalex.org/W1518705996","https://openalex.org/W1519337070","https://openalex.org/W1612810659","https://openalex.org/W1966447968","https://openalex.org/W1972065960","https://openalex.org/W1997072334","https://openalex.org/W1998522266","https://openalex.org/W2006553351","https://openalex.org/W2044560939","https://openalex.org/W2060407451","https://openalex.org/W2078740228","https://openalex.org/W2080267935","https://openalex.org/W2088086751","https://openalex.org/W2093912331","https://openalex.org/W2100465945","https://openalex.org/W2101625939","https://openalex.org/W2102128707","https://openalex.org/W2103240723","https://openalex.org/W2111368429","https://openalex.org/W2114766961","https://openalex.org/W2119027206","https://openalex.org/W2122479308","https://openalex.org/W2129369779","https://openalex.org/W2139691310","https://openalex.org/W2140132043","https://openalex.org/W2142785340","https://openalex.org/W2150612825","https://openalex.org/W2152056125","https://openalex.org/W2152406824","https://openalex.org/W2153780507","https://openalex.org/W2154838247","https://openalex.org/W2158673063","https://openalex.org/W2164154623","https://openalex.org/W2166795801","https://openalex.org/W2167010012","https://openalex.org/W2169228666","https://openalex.org/W3151969339"],"related_works":["https://openalex.org/W2131164334","https://openalex.org/W3141532631","https://openalex.org/W1568384982","https://openalex.org/W4249396218","https://openalex.org/W2124007265","https://openalex.org/W2080423274","https://openalex.org/W1564702418","https://openalex.org/W4288044863","https://openalex.org/W1995176744","https://openalex.org/W1745650241"],"abstract_inverted_index":{"Classical":[0],"two-variable":[1],"symmetries":[2,43],"play":[3],"an":[4],"important":[5],"role":[6],"in":[7,50],"many":[8],"EDA":[9],"applications,":[10],"ranging":[11],"from":[12],"logic":[13],"synthesis":[14],"to":[15,52],"formal":[16],"verification.":[17],"This":[18,48],"paper":[19],"proposes":[20],"a":[21],"complete":[22,58],"circuit-based":[23,55],"method":[24,67],"that":[25,64],"makes":[26],"uses":[27],"of":[28,41,44],"structural":[29],"analysis,":[30],"integrated":[31],"simulation":[32],"and":[33,38,57],"Boolean":[34,46,71],"satisfiability":[35],"for":[36,69,73],"fast":[37],"scalable":[39],"detection":[40],"classical":[42],"completely-specified":[45],"functions.":[47],"is":[49],"contrast":[51],"previous":[53],"incomplete":[54],"methods":[56],"BDD-based":[59],"methods.":[60],"Experimental":[61],"results":[62],"demonstrate":[63],"the":[65],"proposed":[66],"works":[68],"large":[70],"functions,":[72],"which":[74],"BDDs":[75],"cannot":[76],"be":[77],"constructed.":[78]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-10T00:00:00"}