{"id":"https://openalex.org/W7158719224","doi":"https://doi.org/10.48550/arxiv.2604.26364","title":"Automaton-based Characterisations of First Order Logic over Infinite Trees","display_name":"Automaton-based Characterisations of First Order Logic over Infinite Trees","publication_year":2026,"publication_date":"2026-04-29","ids":{"openalex":"https://openalex.org/W7158719224","doi":"https://doi.org/10.48550/arxiv.2604.26364"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.26364","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.26364","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.26364","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048258273","display_name":"Massimo Benerecetti","orcid":"https://orcid.org/0000-0003-4664-6061"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Benerecetti, Massimo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033663075","display_name":"Dario Della Monica","orcid":"https://orcid.org/0000-0001-9743-665X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Della Monica, Dario","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103515329","display_name":"Angelo Matteo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matteo, Angelo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052215915","display_name":"Fabio Mogavero","orcid":"https://orcid.org/0000-0002-5140-5783"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mogavero, Fabio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5105824253","display_name":"Gabriele Puppis","orcid":"https://orcid.org/0000-0001-9831-3264"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Puppis, Gabriele","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5048258273"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.7063999772071838,"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":0.7063999772071838,"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":0.08150000125169754,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.0794999971985817,"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/expressive-power","display_name":"Expressive power","score":0.7228000164031982},{"id":"https://openalex.org/keywords/first-order","display_name":"First order","score":0.4934000074863434},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.490200012922287},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.47209998965263367},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4699000120162964},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.4593000113964081},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.37880000472068787},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37459999322891235}],"concepts":[{"id":"https://openalex.org/C195818886","wikidata":"https://www.wikidata.org/wiki/Q5421724","display_name":"Expressive power","level":2,"score":0.7228000164031982},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6392999887466431},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.4934000074863434},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.490200012922287},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.47209998965263367},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4699000120162964},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.4593000113964081},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4212999939918518},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37770000100135803},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37459999322891235},{"id":"https://openalex.org/C138888516","wikidata":"https://www.wikidata.org/wiki/Q2266843","display_name":"Infinite product","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C198008173","wikidata":"https://www.wikidata.org/wiki/Q1040040","display_name":"Computation tree logic","level":3,"score":0.3147999942302704},{"id":"https://openalex.org/C25016198","wikidata":"https://www.wikidata.org/wiki/Q781833","display_name":"Temporal logic","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.2955000102519989},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.2897000014781952},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25459998846054077},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2517000138759613},{"id":"https://openalex.org/C134121241","wikidata":"https://www.wikidata.org/wiki/Q899301","display_name":"Yield (engineering)","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.26364","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.26364","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.26364","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.26364","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,14,33,36,60,100],"expressive":[3,61,143],"power":[4,62],"of":[5,16,22,50,63,73,104,108,120],"First-Order":[6],"Logic":[7],"(\\FO)":[8],"over":[9,84,148],"(unordered)":[10],"infinite":[11,85,149],"trees,":[12],"with":[13],"aim":[15],"identifying":[17],"robust":[18],"characterisations":[19,92],"in":[20,32,102,122],"terms":[21,103],"branching-time":[23,37,65],"specification":[24],"formalisms.":[25],"While":[26],"such":[27],"correspondences":[28],"are":[29,134],"well":[30],"understood":[31],"linear-time":[34],"setting,":[35],"case":[38],"presents":[39],"well-known":[40],"structural":[41],"challenges.":[42],"To":[43],"this":[44,123],"end,":[45],"we":[46,115],"introduce":[47],"two":[48,64],"classes":[49],"hesitant":[51],"tree":[52],"automata":[53],"and":[54,70,93],"show":[55],"that":[56,133],"they":[57],"capture":[58],"precisely":[59],"temporal":[66],"logics,":[67],"namely":[68],"\\PolPCTL":[69],"\\CTLsf,":[71],"both":[72],"which":[74],"have":[75],"been":[76],"previously":[77],"shown":[78],"to":[79,82],"be":[80],"equivalent":[81],"\\FO":[83,121],"trees.":[86,150],"These":[87],"results":[88],"provide":[89],"uniform":[90],"automata-theoretic":[91],"yield":[94],"a":[95,105,113,117,141],"natural":[96],"normal":[97],"form":[98],"for":[99,145],"latter":[101],"new":[106],"fragment":[107],"\\CTLs":[109],"called":[110],"\\PolCTLs.":[111],"As":[112],"consequence,":[114],"identify":[116],"fundamental":[118],"limitation":[119],"setting:":[124],"along":[125],"each":[126],"branch,":[127],"it":[128],"can":[129],"express":[130],"only":[131],"properties":[132],"either":[135],"safety":[136],"or":[137],"co-safety,":[138],"thereby":[139],"revealing":[140],"sharp":[142],"boundary":[144],"first-order":[146],"definability":[147]},"counts_by_year":[],"updated_date":"2026-05-01T06:10:29.291645","created_date":"2026-05-01T00:00:00"}
