{"id":"https://openalex.org/W1590873873","doi":"https://doi.org/10.25596/jalc-2005-079","title":"Gr\u00f6bner Bases and the Defining Polynomial of a Context-Free Grammar Generating Function","display_name":"Gr\u00f6bner Bases and the Defining Polynomial of a Context-Free Grammar Generating Function","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1590873873","doi":"https://doi.org/10.25596/jalc-2005-079","mag":"1590873873"},"language":"en","primary_location":{"id":"doi:10.25596/jalc-2005-079","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2005-079","pdf_url":null,"source":{"id":"https://openalex.org/S62907800","display_name":"Journal of automata, languages and combinatorics","issn_l":"1430-189X","issn":["1430-189X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313929","host_organization_name":"University of Giessen","host_organization_lineage":["https://openalex.org/P4310313929"],"host_organization_lineage_names":["University of Giessen"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://doi.org/10.25596/jalc-2005-079","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030848660","display_name":"Alois Panholzer","orcid":"https://orcid.org/0000-0003-2813-3457"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Panholzer, Alois","raw_affiliation_strings":["Institut f\u00fcr Diskrete Mathematik Und Geometrie, Technische Universit\u00e4t Wien, Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Diskrete Mathematik Und Geometrie, Technische Universit\u00e4t Wien, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030848660"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":null,"apc_paid":null,"fwci":0.6373,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.68411718,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"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/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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":0.9940000176429749,"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/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.772636890411377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6728522777557373},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5951247215270996},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.566176176071167},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5436742305755615},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.5434539318084717},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5371668338775635},{"id":"https://openalex.org/keywords/algebraic-function","display_name":"Algebraic function","score":0.5294924378395081},{"id":"https://openalex.org/keywords/context-free-grammar","display_name":"Context-free grammar","score":0.4985158443450928},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47053417563438416},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.47040945291519165},{"id":"https://openalex.org/keywords/grammar","display_name":"Grammar","score":0.44550031423568726},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41858065128326416},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3770560324192047},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36931753158569336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3026689887046814},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.14300808310508728},{"id":"https://openalex.org/keywords/parsing","display_name":"Parsing","score":0.09606719017028809}],"concepts":[{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.772636890411377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6728522777557373},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5951247215270996},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.566176176071167},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5436742305755615},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.5434539318084717},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5371668338775635},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.5294924378395081},{"id":"https://openalex.org/C97212296","wikidata":"https://www.wikidata.org/wiki/Q338047","display_name":"Context-free grammar","level":3,"score":0.4985158443450928},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47053417563438416},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.47040945291519165},{"id":"https://openalex.org/C26022165","wikidata":"https://www.wikidata.org/wiki/Q8091","display_name":"Grammar","level":2,"score":0.44550031423568726},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41858065128326416},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3770560324192047},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36931753158569336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3026689887046814},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14300808310508728},{"id":"https://openalex.org/C186644900","wikidata":"https://www.wikidata.org/wiki/Q194152","display_name":"Parsing","level":2,"score":0.09606719017028809},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.25596/jalc-2005-079","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2005-079","pdf_url":null,"source":{"id":"https://openalex.org/S62907800","display_name":"Journal of automata, languages and combinatorics","issn_l":"1430-189X","issn":["1430-189X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313929","host_organization_name":"University of Giessen","host_organization_lineage":["https://openalex.org/P4310313929"],"host_organization_lineage_names":["University of Giessen"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.25596/jalc-2005-079","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2005-079","pdf_url":null,"source":{"id":"https://openalex.org/S62907800","display_name":"Journal of automata, languages and combinatorics","issn_l":"1430-189X","issn":["1430-189X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313929","host_organization_name":"University of Giessen","host_organization_lineage":["https://openalex.org/P4310313929"],"host_organization_lineage_names":["University of Giessen"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[{"display_name":"Quality Education","score":0.47999998927116394,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W36566811","https://openalex.org/W145236249","https://openalex.org/W1561016548","https://openalex.org/W1578332044","https://openalex.org/W1890888469","https://openalex.org/W2018273673","https://openalex.org/W2031399497","https://openalex.org/W2070190750"],"related_works":["https://openalex.org/W3014248351","https://openalex.org/W2340541605","https://openalex.org/W1552875110","https://openalex.org/W1998797986","https://openalex.org/W2894259695","https://openalex.org/W3103027124","https://openalex.org/W27516335","https://openalex.org/W1996632762","https://openalex.org/W45149845","https://openalex.org/W2594439144","https://openalex.org/W77534004","https://openalex.org/W2031399497","https://openalex.org/W61796042","https://openalex.org/W2112632181","https://openalex.org/W2079751279","https://openalex.org/W2517219774","https://openalex.org/W2094272047","https://openalex.org/W149165626","https://openalex.org/W2095647738","https://openalex.org/W1753062909"],"abstract_inverted_index":{"We":[0,79],"consider":[1],"proper":[2],"algebraic":[3,43,98,115],"systems":[4],"as":[5],"defined":[6],"in":[7,56,82],"[7]":[8],"and":[9,99],"reprove":[10,80],"via":[11,76],"Gr{\\\"{o}}bner":[12,70],"bases":[13],"algorithms":[14],"that":[15,86,101],"the":[16,28,37,51,66,87,102],"quasiregular":[17],"solution":[18],"of":[19,32,40,68,72,90,93,105],"such":[20],"a":[21,33,69,83,94,106],"system":[22],"is":[23,97,114],"algebraic.":[24],"In":[25],"this":[26],"context,":[27],"effective":[29,38],"primary":[30],"decomposition":[31,39],"polynomial":[34],"ideal":[35,75],"resp.":[36],"an":[41,73,110],"affine":[42],"variety":[44],"into":[45],"irreducible":[46],"components":[47],"are":[48,63],"alternatives":[49],"to":[50],"Kuich-Salomaa":[52],"elimination":[53,74],"algorithm":[54],"described":[55],"[7].":[57],"Both":[58],"here":[59],"applied":[60],"decom-":[61],"positions":[62],"based":[64],"on":[65],"construction":[67],"basis":[71],"Buchberger's":[77],"algorithm.":[78],"then":[81],"constructive":[84],"way":[85],"generating":[88,103],"function":[89,104],"each":[91],"nonterminal":[92],"context-free":[95,112],"grammar":[96,113],"also":[100],"language,":[107],"generated":[108],"by":[109],"unambiguous":[111],"(Chomsky-Sch{\\\"{u}}tzenberger":[116],"[4]).":[117]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2016-06-24T00:00:00"}