{"id":"https://openalex.org/W4400920795","doi":"https://doi.org/10.46298/lmcs-20(3:9)2024","title":"Coalgebraic Satisfiability Checking for Arithmetic $\\mu$-Calculi","display_name":"Coalgebraic Satisfiability Checking for Arithmetic $\\mu$-Calculi","publication_year":2024,"publication_date":"2024-07-23","ids":{"openalex":"https://openalex.org/W4400920795","doi":"https://doi.org/10.46298/lmcs-20(3:9)2024"},"language":"en","primary_location":{"id":"doi:10.46298/lmcs-20(3:9)2024","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-20(3:9)2024","pdf_url":"https://lmcs.episciences.org/13967/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/13967/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068252968","display_name":"Daniel Hausmann","orcid":"https://orcid.org/0000-0002-0935-8602"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Daniel Hausmann","raw_affiliation_strings":["University of Liverpool, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Liverpool, United Kingdom","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073765060","display_name":"Lutz Schr\u00f6der","orcid":"https://orcid.org/0000-0002-3146-5906"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lutz Schr\u00f6der","raw_affiliation_strings":["Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Germany"],"affiliations":[{"raw_affiliation_string":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068252968"],"corresponding_institution_ids":["https://openalex.org/I146655781"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09308562,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Volume 20, Issue 3","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.994700014591217,"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/T10126","display_name":"Logic, programming, and type systems","score":0.994700014591217,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9930999875068665,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9871000051498413,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.7082456350326538},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.7033158540725708},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5197893381118774},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4471094608306885},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4129272699356079},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3590713143348694}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7082456350326538},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.7033158540725708},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5197893381118774},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4471094608306885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4129272699356079},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3590713143348694}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46298/lmcs-20(3:9)2024","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-20(3:9)2024","pdf_url":"https://lmcs.episciences.org/13967/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ef01bde5e1b64ea3bb26fc62fdc6ff56","is_oa":true,"landing_page_url":"https://doaj.org/article/ef01bde5e1b64ea3bb26fc62fdc6ff56","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 20, Issue 3 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46298/lmcs-20(3:9)2024","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-20(3:9)2024","pdf_url":"https://lmcs.episciences.org/13967/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3074649572","display_name":"Lazy Synthesis Techniques","funder_award_id":"EP/Z003121/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3917955685","display_name":"Koalgebraische Deduktionssysteme f\u00fcr quantitative Systemanalyse","funder_award_id":"531706730","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6743243744","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8452545418","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"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/W4400920795.pdf","grobid_xml":"https://content.openalex.org/works/W4400920795.grobid-xml"},"referenced_works_count":82,"referenced_works":["https://openalex.org/W187636597","https://openalex.org/W193053345","https://openalex.org/W1497670448","https://openalex.org/W1501952738","https://openalex.org/W1507873625","https://openalex.org/W1510355981","https://openalex.org/W1543688617","https://openalex.org/W1557881307","https://openalex.org/W1564580204","https://openalex.org/W1576921484","https://openalex.org/W1594196576","https://openalex.org/W1597481850","https://openalex.org/W1981607181","https://openalex.org/W1982431152","https://openalex.org/W1998546048","https://openalex.org/W2015640848","https://openalex.org/W2026405784","https://openalex.org/W2030418131","https://openalex.org/W2031592188","https://openalex.org/W2031830176","https://openalex.org/W2048905609","https://openalex.org/W2049154590","https://openalex.org/W2050073538","https://openalex.org/W2051491228","https://openalex.org/W2060688311","https://openalex.org/W2060917500","https://openalex.org/W2067754486","https://openalex.org/W2077519384","https://openalex.org/W2077974960","https://openalex.org/W2083398633","https://openalex.org/W2087403174","https://openalex.org/W2088027070","https://openalex.org/W2088189323","https://openalex.org/W2091027967","https://openalex.org/W2103774282","https://openalex.org/W2108446683","https://openalex.org/W2112476716","https://openalex.org/W2115452397","https://openalex.org/W2116277209","https://openalex.org/W2121827343","https://openalex.org/W2123876422","https://openalex.org/W2139315517","https://openalex.org/W2142018979","https://openalex.org/W2166510793","https://openalex.org/W2169250070","https://openalex.org/W2170319925","https://openalex.org/W2170933628","https://openalex.org/W2172114884","https://openalex.org/W2176114185","https://openalex.org/W2241580932","https://openalex.org/W2250074872","https://openalex.org/W2311027344","https://openalex.org/W2467982476","https://openalex.org/W2502103274","https://openalex.org/W2531137472","https://openalex.org/W2898545346","https://openalex.org/W2908449277","https://openalex.org/W2912640545","https://openalex.org/W2950206012","https://openalex.org/W2952147691","https://openalex.org/W2963082232","https://openalex.org/W2963435309","https://openalex.org/W2963476787","https://openalex.org/W2963537255","https://openalex.org/W2964046005","https://openalex.org/W3015776104","https://openalex.org/W3048737918","https://openalex.org/W3081939111","https://openalex.org/W3103221701","https://openalex.org/W3122950708","https://openalex.org/W3147573360","https://openalex.org/W3189472968","https://openalex.org/W4205825473","https://openalex.org/W4206087489","https://openalex.org/W4211144022","https://openalex.org/W4213277014","https://openalex.org/W4232922275","https://openalex.org/W4248784701","https://openalex.org/W4287630470","https://openalex.org/W4301808069","https://openalex.org/W4302155065","https://openalex.org/W4386363652"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W3037419933","https://openalex.org/W44982509","https://openalex.org/W2952234674","https://openalex.org/W1543051890"],"abstract_inverted_index":{"The":[0,167],"coalgebraic":[1,31],"$\\mu$-calculus":[2,32,213,230],"provides":[3],"a":[4,59,172],"generic":[5,173],"semantic":[6],"framework":[7],"for":[8,50,92,152,204],"fixpoint":[9],"logics":[10],"over":[11],"systems":[12],"whose":[13],"branching":[14],"type":[15],"goes":[16],"beyond":[17],"the":[18,30,45,51,75,79,116,128,133,144,147,153,160,165,194,211,227],"standard":[19],"relational":[20],"setup,":[21],"e.g.":[22],"probabilistic,":[23],"weighted,":[24],"or":[25,119],"game-based.":[26],"Previous":[27],"work":[28],"on":[29,38,44],"includes":[33],"an":[34,208,224],"exponential-time":[35,201],"upper":[36,135,202],"bound":[37,137,168],"satisfiability":[39,150,180,205],"checking,":[40],"which":[41],"however":[42],"relies":[43],"availability":[46],"of":[47,78,105,146,164,193,210,226],"tableau":[48],"rules":[49,80],"next-step":[52,162],"modalities":[53],"that":[54,177],"are":[55,97],"sufficiently":[56],"well-behaved":[57],"in":[58,63,102,107,115,122,207],"formally":[60],"defined":[61],"sense;":[62],"particular,":[64],"rule":[65,87],"matches":[66],"need":[67,81],"to":[68,82,100],"be":[69],"representable":[70],"by":[71,171],"polynomial-sized":[72],"codes,":[73],"and":[74,189],"sequent":[76],"duals":[77],"absorb":[83],"cut.":[84],"While":[85],"such":[86],"sets":[88],"have":[89],"been":[90],"identified":[91],"some":[93],"important":[94],"cases,":[95],"they":[96],"not":[98],"known":[99],"exist":[101],"all":[103],"cases":[104],"interest,":[106],"particular":[108],"ones":[109],"involving":[110],"either":[111],"integer":[112],"weights":[113,121],"as":[114,159,221,223],"graded":[117,212],"$\\mu$-calculus,":[118],"real-valued":[120],"combination":[123],"with":[124,214,231],"non-linear":[125],"arithmetic.":[126],"In":[127],"present":[129],"work,":[130],"we":[131],"prove":[132],"same":[134],"complexity":[136,145],"under":[138],"more":[139],"general":[140],"assumptions,":[141],"specifically":[142],"regarding":[143],"(much":[148],"simpler)":[149],"problem":[151],"underlying":[154],"one-step":[155],"logic,":[156],"roughly":[157],"described":[158],"nesting-free":[161],"fragment":[163],"logic.":[166],"is":[169],"realized":[170],"global":[174],"caching":[175],"algorithm":[176],"supports":[178],"on-the-fly":[179],"checking.":[181],"Notably,":[182],"our":[183],"approach":[184],"directly":[185],"accommodates":[186],"unguarded":[187],"formulae,":[188],"thus":[190],"avoids":[191],"use":[192],"guardedness":[195],"transformation.":[196],"Example":[197],"applications":[198],"include":[199],"new":[200],"bounds":[203],"checking":[206],"extension":[209,225],"polynomial":[215,232],"inequalities":[216],"(including":[217],"positive":[218],"Presburger":[219],"arithmetic),":[220],"well":[222],"(two-valued)":[228],"probabilistic":[229],"inequalities.":[233]},"counts_by_year":[],"updated_date":"2026-03-25T14:56:36.534964","created_date":"2025-10-10T00:00:00"}