{"id":"https://openalex.org/W7081913288","doi":"https://doi.org/10.1007/978-3-032-04167-8_12","title":"Graph-Embedded Rewrite Systems: Combination and\u00a0Undecidability Results","display_name":"Graph-Embedded Rewrite Systems: Combination and\u00a0Undecidability Results","publication_year":2025,"publication_date":"2025-09-14","ids":{"openalex":"https://openalex.org/W7081913288","doi":"https://doi.org/10.1007/978-3-032-04167-8_12"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-032-04167-8_12","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-04167-8_12","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-04167-8_12.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-04167-8_12.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Serdar Erbatur","orcid":"https://orcid.org/0000-0002-7574-195X"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Serdar Erbatur","raw_affiliation_strings":["University of Texas at Dallas, Richardson, TX, USA"],"raw_orcid":"https://orcid.org/0000-0002-7574-195X","affiliations":[{"raw_affiliation_string":"University of Texas at Dallas, Richardson, TX, USA","institution_ids":["https://openalex.org/I162577319"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Andrew M. Marshall","orcid":"https://orcid.org/0000-0002-0522-8384"},"institutions":[{"id":"https://openalex.org/I191484440","display_name":"University of Mary Washington","ror":"https://ror.org/03b48gv34","country_code":"US","type":"education","lineage":["https://openalex.org/I191484440"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew M. Marshall","raw_affiliation_strings":["University of Mary Washington, Fredericksburg, VA, USA"],"raw_orcid":"https://orcid.org/0000-0002-0522-8384","affiliations":[{"raw_affiliation_string":"University of Mary Washington, Fredericksburg, VA, USA","institution_ids":["https://openalex.org/I191484440"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Paliath Narendran","orcid":"https://orcid.org/0000-0003-4521-5892"},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paliath Narendran","raw_affiliation_strings":["University at Albany, SUNY, Albany, NY, USA"],"raw_orcid":"https://orcid.org/0000-0003-4521-5892","affiliations":[{"raw_affiliation_string":"University at Albany, SUNY, Albany, NY, USA","institution_ids":["https://openalex.org/I392282"]}]},{"author_position":"last","author":{"id":null,"display_name":"Christophe Ringeissen","orcid":"https://orcid.org/0000-0002-5937-6059"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Ringeissen","raw_affiliation_strings":["Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, 54000, Nancy, France"],"raw_orcid":"https://orcid.org/0000-0002-5937-6059","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, 54000, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I90183372","https://openalex.org/I4210121838"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I162577319"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.70604508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"209","last_page":"227"},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.6937000155448914,"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"}},"topics":[{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.6937000155448914,"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/T13067","display_name":"Geological Modeling and Analysis","score":0.027400000020861626,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14311","display_name":"Electrical and Electromagnetic Research","score":0.01679999940097332,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.9010000228881836},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5683000087738037},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5217000246047974},{"id":"https://openalex.org/keywords/decision-problem","display_name":"Decision problem","score":0.3824999928474426},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.37059998512268066},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.366100013256073}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.9010000228881836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7939000129699707},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5683000087738037},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5217000246047974},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.398499995470047},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.3824999928474426},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.366100013256073},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31929999589920044},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31929999589920044},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.31360000371932983},{"id":"https://openalex.org/C2987117450","wikidata":"https://www.wikidata.org/wiki/Q275603","display_name":"Logic program","level":3,"score":0.3109000027179718},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C98183937","wikidata":"https://www.wikidata.org/wiki/Q2112188","display_name":"Program analysis","level":2,"score":0.2599000036716461}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-032-04167-8_12","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-04167-8_12","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-04167-8_12.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:hal-05324986v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05324986","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://icetcs.github.io/frocos-itp-tableaux25/frocos/","raw_type":"Conference papers"}],"best_oa_location":{"id":"doi:10.1007/978-3-032-04167-8_12","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-04167-8_12","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-04167-8_12.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"score":0.6817971467971802,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7081913288.pdf","grobid_xml":"https://content.openalex.org/works/W7081913288.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1536580911","https://openalex.org/W1543811964","https://openalex.org/W1566539263","https://openalex.org/W1598111807","https://openalex.org/W1603878273","https://openalex.org/W1973054120","https://openalex.org/W1991537775","https://openalex.org/W2002789557","https://openalex.org/W2036714652","https://openalex.org/W2042924775","https://openalex.org/W2057936571","https://openalex.org/W2060349224","https://openalex.org/W2114189125","https://openalex.org/W2117064875","https://openalex.org/W2126338744","https://openalex.org/W2133126578","https://openalex.org/W2138196723","https://openalex.org/W2162325770","https://openalex.org/W2521663436","https://openalex.org/W2589748073","https://openalex.org/W2735210188","https://openalex.org/W2741014554","https://openalex.org/W3010382948","https://openalex.org/W3022449549","https://openalex.org/W4230919050","https://openalex.org/W4393339567","https://openalex.org/W4402309992"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,131],"paper,":[3],"we":[4,79],"consider":[5,80],"the":[6,15,35,81,87,118,140,143,184,197,200,224],"knowledge":[7],"problems":[8,33,162],"of":[9,18,75,99,134,168,183,195,199,223],"deduction":[10,148,213],"and":[11,65,149,153,179,214],"static":[12,215],"equivalence":[13],"in":[14,34],"formal":[16],"analysis":[17],"security":[19],"protocols.":[20],"We":[21,115,137,188,217],"extend":[22],"a":[23,28,53,72,97,127,154,221],"recent":[24],"result":[25],"that":[26,117,190,220],"developed":[27],"decision":[29,120],"procedure":[30,121],"for":[31,130,146,159,212],"these":[32,161],"non-disjoint":[36],"combination":[37,83],"$$R":[38],"\\cup":[39],"E$$":[40],"<mml:math":[41,56,67,90,102,110],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[42,57,68,91,103,111],"<mml:mrow>":[43],"<mml:mi>R</mml:mi>":[44],"<mml:mo>\u222a</mml:mo>":[45],"<mml:mi>E</mml:mi>":[46,58,69,92,104,112],"</mml:mrow>":[47],"</mml:math>":[48,59,70,93,105,113],",":[49],"where":[50],"R":[51],"is":[52,71,167,227],"subterm":[54,88,100],"$$E$$":[55,66,89,101,109],"-convergent":[60,94],"term":[61],"rewrite":[62],"system":[63],"(TRS)":[64],"restricted":[73],"form":[74],"permutative":[76],"theory.":[77],"Here,":[78],"same":[82],"problem":[84],"but":[85],"replace":[86],"TRS":[95],"with":[96],"superclass":[98,156],"-convergent,":[106],"called":[107,157],"contracting":[108,144,201],"-convergent.":[114],"show":[116,189,219],"previous":[119],"can":[122],"be":[123],"extended":[124],"to":[125,174,177,209,230],"obtain":[126,231],"new":[128],"algorithm":[129],"larger":[132,155],"class":[133],"combined":[135],"theories.":[136],"also":[138,218],"explore":[139],"gap":[141,166],"between":[142],"TRSs,":[145],"which":[147,160],"static-equivalence":[150],"are":[151,163],"decidable,":[152],"graph-embedded":[158,178,225],"undecidable.":[164],"This":[165],"interest":[169],"since":[170],"one":[171,193],"would":[172],"like":[173],"get":[175],"closer":[176],"still":[180,228],"maintain":[181],"decidability":[182],"above":[185],"\u201cknowledge":[186],"problems.\u201d":[187],"at":[191],"least":[192],"way":[194],"weakening":[196],"restrictions":[198],"definition":[202],"will":[203],"not":[204],"work,":[205],"as":[206],"it":[207],"leads":[208],"undecidability":[210],"results":[211],"equivalence.":[216],"subset":[222],"rules":[226],"sufficient":[229],"undecidability.":[232]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}