{"id":"https://openalex.org/W3211980671","doi":"https://doi.org/10.1007/978-3-030-99253-8_6","title":"Graphical Piecewise-Linear Algebra","display_name":"Graphical Piecewise-Linear Algebra","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W3211980671","doi":"https://doi.org/10.1007/978-3-030-99253-8_6","mag":"3211980671"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-99253-8_6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99253-8_6","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_6.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":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056706196","display_name":"Guillaume Boisseau","orcid":"https://orcid.org/0000-0001-5244-893X"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Guillaume Boisseau","raw_affiliation_strings":["University of Oxford, Oxford, UK"],"raw_orcid":"https://orcid.org/0000-0001-5244-893X","affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012245406","display_name":"Robin Piedeleu","orcid":"https://orcid.org/0000-0002-3945-2704"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Robin Piedeleu","raw_affiliation_strings":["University College London, London, UK"],"raw_orcid":"https://orcid.org/0000-0002-3945-2704","affiliations":[{"raw_affiliation_string":"University College London, London, UK","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056706196"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.8699,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84083402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"101","last_page":"119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9995999932289124,"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":0.9995999932289124,"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/T11125","display_name":"Petri Nets in System Modeling","score":0.9983999729156494,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9944000244140625,"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/diagrammatic-reasoning","display_name":"Diagrammatic reasoning","score":0.698459804058075},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5337504148483276},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5319955945014954},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5257193446159363},{"id":"https://openalex.org/keywords/petri-net","display_name":"Petri net","score":0.5215948820114136},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.45337435603141785},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.42479363083839417},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.4134441018104553},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4088031053543091},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35805028676986694},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2976182699203491},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2914745807647705},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.27095264196395874}],"concepts":[{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.698459804058075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5337504148483276},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5319955945014954},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5257193446159363},{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.5215948820114136},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.45337435603141785},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.42479363083839417},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.4134441018104553},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4088031053543091},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35805028676986694},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2976182699203491},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2914745807647705},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.27095264196395874},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-99253-8_6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99253-8_6","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_6.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"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-99253-8_6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99253-8_6","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_6.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":[],"awards":[{"id":"https://openalex.org/G4854729358","display_name":null,"funder_award_id":"EP/V002376/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7698081211","display_name":"Nominal String Diagrams","funder_award_id":"EP/V002376/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3211980671.pdf","grobid_xml":"https://content.openalex.org/works/W3211980671.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1514879827","https://openalex.org/W2135956037","https://openalex.org/W2148443868","https://openalex.org/W2152476038","https://openalex.org/W2737072409","https://openalex.org/W2773827414","https://openalex.org/W2799037673","https://openalex.org/W2900110008","https://openalex.org/W2965266081","https://openalex.org/W3164515596","https://openalex.org/W3166645774","https://openalex.org/W4213284502"],"related_works":["https://openalex.org/W3003518673","https://openalex.org/W2243494072","https://openalex.org/W3083799684","https://openalex.org/W2933723564","https://openalex.org/W4288417689","https://openalex.org/W1582653816","https://openalex.org/W3036486735","https://openalex.org/W4388991336","https://openalex.org/W2134137410","https://openalex.org/W1785591160"],"abstract_inverted_index":{"Abstract":[0],"Graphical":[1,54,109],"(Linear)":[2],"Algebra":[3],"is":[4,117],"a":[5,57,77,103,123,144],"family":[6,47],"of":[7,16,18,64,71,108,125,137,141,152],"diagrammatic":[8,154],"languages":[9],"allowing":[10],"to":[11,26,34,45,52,60,86],"reason":[12,87],"about":[13,88],"different":[14],"kinds":[15],"subsets":[17,63],"vector":[19,65],"spaces":[20],"compositionally.":[21],"It":[22],"has":[23],"been":[24],"used":[25,85],"model":[27],"various":[28],"application":[29],"domains,":[30],"from":[31],"signal-flow":[32],"graphs":[33],"Petri":[35],"nets":[36],"and":[37,112],"electrical":[38],"circuits.":[39],"In":[40],"this":[41,115],"paper,":[42],"we":[43,129],"introduce":[44],"the":[46,68,72,89,96,118,135,150],"its":[48,131],"most":[49],"expressive":[50],"member":[51],"date:":[53],"Piecewise-Linear":[55],"Algebra,":[56,111],"new":[58],"language":[59],"specify":[61],"piecewise-linear":[62],"spaces.":[66],"Like":[67],"previous":[69,153],"members":[70],"family,":[73],"it":[74,82],"comes":[75],"with":[76],"complete":[78],"axiomatisation,":[79],"which":[80],"means":[81],"can":[83,121],"be":[84],"corresponding":[90],"semantic":[91],"domain":[92,145],"purely":[93],"equationally,":[94],"forgetting":[95],"set-theoretic":[97],"interpretation.":[98],"We":[99],"show":[100,113],"completeness":[101],"using":[102],"single":[104],"axiom":[105],"on":[106],"top":[107],"Polyhedral":[110],"that":[114,120,146],"extension":[116],"smallest":[119],"capture":[122],"variety":[124],"relevant":[126],"constructs.":[127],"Finally,":[128],"showcase":[130],"use":[132],"by":[133],"modelling":[134],"behaviour":[136],"stateless":[138],"electronic":[139],"circuits":[140],"ideal":[142],"elements,":[143],"had":[147],"remained":[148],"outside":[149],"remit":[151],"languages.":[155]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}