{"id":"https://openalex.org/W2772805889","doi":"https://doi.org/10.1017/s096012951700024x","title":"Paths, tree homomorphisms and disequalities for -clauses","display_name":"Paths, tree homomorphisms and disequalities for -clauses","publication_year":2017,"publication_date":"2017-12-06","ids":{"openalex":"https://openalex.org/W2772805889","doi":"https://doi.org/10.1017/s096012951700024x","mag":"2772805889"},"language":"en","primary_location":{"id":"doi:10.1017/s096012951700024x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096012951700024x","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057947222","display_name":"Andreas Reu\u00df","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"ANDREAS REU\u00df","raw_affiliation_strings":["Institut f\u00fcr Informatik I2, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstra\u00dfe 3, D-85748 Garching, Germany Emails:"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik I2, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstra\u00dfe 3, D-85748 Garching, Germany Emails:","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080676686","display_name":"Helmut Seidl","orcid":"https://orcid.org/0000-0002-2135-1593"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"HELMUT SEIDL","raw_affiliation_strings":["Institut f\u00fcr Informatik I2, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstra\u00dfe 3, D-85748 Garching, Germany Emails:"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik I2, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstra\u00dfe 3, D-85748 Garching, Germany Emails:","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057947222"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16904315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"10","first_page":"1786","last_page":"1846"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9977999925613403,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9977999925613403,"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/T11567","display_name":"semigroups and automata theory","score":0.9973999857902527,"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/T10142","display_name":"Formal Methods in Verification","score":0.9958999752998352,"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/decidability","display_name":"Decidability","score":0.807531476020813},{"id":"https://openalex.org/keywords/horn-clause","display_name":"Horn clause","score":0.6756628155708313},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.6625066995620728},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5532507300376892},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5427097082138062},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5121817588806152},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49861860275268555},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.47896960377693176},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47111037373542786},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.47066840529441833},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4542650580406189},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.44787296652793884},{"id":"https://openalex.org/keywords/pushdown-automaton","display_name":"Pushdown automaton","score":0.44619470834732056},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42653876543045044},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.29452067613601685},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.23387017846107483},{"id":"https://openalex.org/keywords/prolog","display_name":"Prolog","score":0.22365200519561768},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.20594891905784607}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.807531476020813},{"id":"https://openalex.org/C189790780","wikidata":"https://www.wikidata.org/wiki/Q933932","display_name":"Horn clause","level":3,"score":0.6756628155708313},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.6625066995620728},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5532507300376892},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5427097082138062},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5121817588806152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49861860275268555},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.47896960377693176},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47111037373542786},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.47066840529441833},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4542650580406189},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.44787296652793884},{"id":"https://openalex.org/C77944639","wikidata":"https://www.wikidata.org/wiki/Q751443","display_name":"Pushdown automaton","level":3,"score":0.44619470834732056},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42653876543045044},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29452067613601685},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.23387017846107483},{"id":"https://openalex.org/C81721847","wikidata":"https://www.wikidata.org/wiki/Q163468","display_name":"Prolog","level":2,"score":0.22365200519561768},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.20594891905784607},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s096012951700024x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096012951700024x","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1479744988","https://openalex.org/W1522049580","https://openalex.org/W1552360561","https://openalex.org/W1553458439","https://openalex.org/W1571999050","https://openalex.org/W1575393813","https://openalex.org/W1581717847","https://openalex.org/W1972507301","https://openalex.org/W1975895350","https://openalex.org/W2000550348","https://openalex.org/W2014118070","https://openalex.org/W2059186017","https://openalex.org/W2114189125","https://openalex.org/W2124548094","https://openalex.org/W2170630946"],"related_works":["https://openalex.org/W2294297515","https://openalex.org/W2585890227","https://openalex.org/W1543051890","https://openalex.org/W2072122432","https://openalex.org/W2789140669","https://openalex.org/W2166108892","https://openalex.org/W1537446812","https://openalex.org/W1541953080","https://openalex.org/W4387885360","https://openalex.org/W419990173"],"abstract_inverted_index":{"It":[0],"is":[1,6,52,144],"well":[2],"known":[3],"that":[4,46,102,126,142],"satisfiability":[5,143],"decidable":[7,133,145],"for":[8,28,48,62,70,103,125,146],"Horn":[9,17,40,49],"clauses":[10,18,50,56],"of":[11,39,75,84,91,107,128],"the":[12,55],"class":[13,127],".":[14],"Since":[15,123],"arbitrary":[16],"can":[19,25,34,120],"naturally":[20],"be":[21,26,35,121],"approximated":[22],"by":[23,37,67,134],"-clauses,":[24],"used":[27],"realizing":[29],"any":[30],"program":[31],"analysis":[32],"which":[33],"specified":[36],"means":[38],"clauses.":[41],"Recently,":[42],"we":[43,87,96,140],"have":[44],"shown":[45,132],"decidability":[47],"from":[51],"retained":[53],"if":[54],"are":[57],"either":[58],"extended":[59,109],"with":[60,110,117,148],"tests":[61,112],"disequality":[63,71],"between":[64,72],"subterms":[65],"identified":[66],"paths":[68],"or":[69],"homomorphic":[73],"images":[74],"terms.":[76],"These":[77],"two":[78],"results":[79],"refer":[80],"to":[81],"orthogonal":[82],"extensions":[83],"-clauses.":[85],"Here,":[86],"provide":[88],"a":[89],"generalization":[90],"both":[92],"results.":[93],"For":[94],"that,":[95],"introduce":[97],"hom-path":[98,118,149],"disequalities":[99,119],"and":[100],"show":[101],"each":[104],"finite":[105],"set":[106],"-clauses":[108,147],"such":[111],"an":[113],"equivalent":[114],"tree":[115],"automaton":[116],"constructed.":[122],"emptiness":[124],"automata":[129],"has":[130],"been":[131],"Godoy":[135],"et":[136],"al.":[137],"in":[138],"2010,":[139],"conclude":[141],"disequalities.":[150]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}