{"id":"https://openalex.org/W2106560469","doi":"https://doi.org/10.1155/2014/352152","title":"Unified Mathematical Framework for Slicing and Symmetry Reduction over Event Structures","display_name":"Unified Mathematical Framework for Slicing and Symmetry Reduction over Event Structures","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2106560469","doi":"https://doi.org/10.1155/2014/352152","mag":"2106560469"},"language":"en","primary_location":{"id":"doi:10.1155/2014/352152","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/352152","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/352152.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/352152.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100956179","display_name":"Xinyan Gao","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinyan Gao","raw_affiliation_strings":["G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102330771","display_name":"Yingcai Ding","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingcai Ding","raw_affiliation_strings":["G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100330675","display_name":"Wen\u2010Bo Liu","orcid":"https://orcid.org/0000-0002-0089-8709"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenbo Liu","raw_affiliation_strings":["G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102144852","display_name":"Kaidi Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaidi Zheng","raw_affiliation_strings":["G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021639720","display_name":"Siyu Huang","orcid":"https://orcid.org/0000-0002-2929-0115"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Siyu Huang","raw_affiliation_strings":["G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101455077","display_name":"Ning Zhou","orcid":"https://orcid.org/0000-0001-7466-8925"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]},{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ning Zhou","raw_affiliation_strings":["School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China","School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"],"raw_orcid":"https://orcid.org/0000-0001-7466-8925","affiliations":[{"raw_affiliation_string":"School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034358133","display_name":"Dakui Li","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dakui Li","raw_affiliation_strings":["G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17071972,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9994000196456909,"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"}},{"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/T12072","display_name":"Machine Learning and Algorithms","score":0.996399998664856,"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/slicing","display_name":"Slicing","score":0.6818525791168213},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.614781379699707},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5765265822410583},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5046027898788452},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.4572070240974426},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.44564828276634216},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.44438862800598145},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42631086707115173},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4086763262748718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3578307032585144},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34946054220199585},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2538163661956787},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24351346492767334},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12914571166038513}],"concepts":[{"id":"https://openalex.org/C2776190703","wikidata":"https://www.wikidata.org/wiki/Q488148","display_name":"Slicing","level":2,"score":0.6818525791168213},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.614781379699707},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5765265822410583},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5046027898788452},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.4572070240974426},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.44564828276634216},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.44438862800598145},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42631086707115173},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4086763262748718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3578307032585144},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34946054220199585},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2538163661956787},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24351346492767334},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12914571166038513},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/352152","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/352152","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/352152.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1412177666","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1412177666","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:352152","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/352152.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:d0eb58a2ea41460ebb046ff01aa1139e","is_oa":true,"landing_page_url":"https://doaj.org/article/d0eb58a2ea41460ebb046ff01aa1139e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/352152","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/352152","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/352152.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4256657879","display_name":null,"funder_award_id":"1600-851025","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6564538579","display_name":null,"funder_award_id":"DUT14QY05","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2106560469.pdf","grobid_xml":"https://content.openalex.org/works/W2106560469.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W53653091","https://openalex.org/W120395894","https://openalex.org/W177313363","https://openalex.org/W1493036753","https://openalex.org/W1512223106","https://openalex.org/W1518546135","https://openalex.org/W1533250466","https://openalex.org/W1536783297","https://openalex.org/W1582426681","https://openalex.org/W1608345513","https://openalex.org/W1885186328","https://openalex.org/W1984801861","https://openalex.org/W1984957636","https://openalex.org/W1991052229","https://openalex.org/W2005281130","https://openalex.org/W2010892521","https://openalex.org/W2020601732","https://openalex.org/W2028661725","https://openalex.org/W2030935018","https://openalex.org/W2037718229","https://openalex.org/W2078120795","https://openalex.org/W2093397547","https://openalex.org/W2098676070","https://openalex.org/W2102059747","https://openalex.org/W2110261509","https://openalex.org/W2117189826","https://openalex.org/W2122859326","https://openalex.org/W2134326845","https://openalex.org/W2141109493","https://openalex.org/W2145777668","https://openalex.org/W2151282032","https://openalex.org/W2166842511","https://openalex.org/W2170797973","https://openalex.org/W2173961470","https://openalex.org/W2470948957","https://openalex.org/W2914421362","https://openalex.org/W4233702006"],"related_works":["https://openalex.org/W2393746923","https://openalex.org/W2972496411","https://openalex.org/W4239223006","https://openalex.org/W3033662781","https://openalex.org/W2137530048","https://openalex.org/W2360869927","https://openalex.org/W2050876785","https://openalex.org/W2074642116","https://openalex.org/W3164401656","https://openalex.org/W2392031372"],"abstract_inverted_index":{"Nonclassical":[0],"slicing":[1,33,98],"and":[2,28,34,44,52,69,73,80,99,102,108,111,128],"symmetry":[3,35,85,100],"reduction":[4,36,47],"can":[5],"act":[6],"as":[7],"efficient":[8],"structural":[9],"abstract":[10],"methods":[11],"for":[12,31,97,131],"pruning":[13],"state":[14],"space":[15],"when":[16],"dealing":[17],"with":[18],"verification":[19,133],"problems.":[20],"In":[21],"this":[22],"paper,":[23],"we":[24,66],"mainly":[25],"address":[26],"theoretical":[27,118,129],"algorithmic":[29],"aspects":[30],"nonclassical":[32],"over":[37],"prime":[38],"event":[39,50,88],"structures.":[40,89],"We":[41,90],"propose":[42],"sliced":[43],"symmetric":[45],"quotient":[46],"models":[48],"of":[49,62,76,87,120],"structures":[51],"present":[53],"their":[54,139],"corresponding":[55],"algorithms.":[56],"To":[57],"construct":[58],"the":[59,63,105],"underlying":[60],"foundation":[61],"proposed":[64],"methodologies,":[65],"introduce":[67],"strong":[68],"weak":[70],"conflict":[71],"concepts":[72],"a":[74,93,117],"pair":[75],"mutually":[77],"inverse":[78],"operators":[79],"extend":[81],"permutation":[82],"group":[83],"based":[84],"notion":[86],"have":[91],"established":[92],"unified":[94],"mathematical":[95],"framework":[96,123],"reduction,":[101],"further":[103],"investigated":[104],"translation,":[106],"isomorphism,":[107],"equivalence":[109],"relationship":[110],"other":[112],"related":[113],"basic":[114],"facts":[115],"from":[116],"point":[119],"view.":[121],"The":[122],"may":[124],"provide":[125],"useful":[126],"guidance":[127],"exploration":[130],"overcoming":[132],"challenges.":[134],"This":[135],"paper":[136],"also":[137],"demonstrates":[138],"practical":[140],"applications":[141],"by":[142],"two":[143],"cases.":[144]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}