{"id":"https://openalex.org/W2066716756","doi":"https://doi.org/10.1080/00207169008803888","title":"Parallel generation of infinite images","display_name":"Parallel generation of infinite images","publication_year":1990,"publication_date":"1990-01-01","ids":{"openalex":"https://openalex.org/W2066716756","doi":"https://doi.org/10.1080/00207169008803888","mag":"2066716756"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169008803888","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5018498749","display_name":"Maurice Nivat","orcid":null},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M Nivat","raw_affiliation_strings":["Universit\u00e9 Paris VII , L.I.T.P., 2 Place de Jussieu, Paris Cedex 05, 75251, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris VII , L.I.T.P., 2 Place de Jussieu, Paris Cedex 05, 75251, France","institution_ids":["https://openalex.org/I204730241"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089834241","display_name":"A. Saoudi","orcid":"https://orcid.org/0000-0003-4422-2054"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A Saoudi","raw_affiliation_strings":["Universit\u00e9 Paris VII , L.I.T.P., 2 Place de Jussieu, Paris Cedex 05, 75251, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris VII , L.I.T.P., 2 Place de Jussieu, Paris Cedex 05, 75251, France","institution_ids":["https://openalex.org/I204730241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034239546","display_name":"V. R. Dare","orcid":"https://orcid.org/0000-0002-0839-6332"},"institutions":[],"countries":["IN"],"is_corresponding":false,"raw_author_name":"V.R Dare","raw_affiliation_strings":["Department of Mathematics , Madras Christian College , Madras, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Madras Christian College , Madras, India","institution_ids":[]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":3,"citation_normalized_percentile":{"value":0.478569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":66,"max":69},"biblio":{"volume":"35","issue":"1-4","first_page":"25","last_page":"42"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9992,"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":0.9992,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9766,"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/T13326","display_name":"Biochemical and Structural Characterization","score":0.9737,"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/finite-set","display_name":"Finite set","score":0.58063096},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5758177},{"id":"https://openalex.org/keywords/infinite-set","display_name":"Infinite set","score":0.41368046}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.75558275},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.70915663},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.6611695},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.60065717},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.58063096},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5758177},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.5441225},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.49769834},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.47882277},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4708041},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4504401},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.41368046},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.41024765},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19542879},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.117262095},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07955167},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169008803888","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.66,"id":"https://metadata.un.org/sdg/4","display_name":"Quality education"}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":21,"referenced_works":["https://openalex.org/W1515587022","https://openalex.org/W1560420247","https://openalex.org/W1608338808","https://openalex.org/W1890888469","https://openalex.org/W1975411323","https://openalex.org/W1976772375","https://openalex.org/W1980080015","https://openalex.org/W1997093946","https://openalex.org/W2025549541","https://openalex.org/W2031365598","https://openalex.org/W2032607679","https://openalex.org/W2033588663","https://openalex.org/W2037185109","https://openalex.org/W2059501879","https://openalex.org/W2067185869","https://openalex.org/W2088892929","https://openalex.org/W2093758017","https://openalex.org/W2094912129","https://openalex.org/W2138856440","https://openalex.org/W2156192120","https://openalex.org/W2167954650"],"related_works":["https://openalex.org/W4210495575","https://openalex.org/W3013502888","https://openalex.org/W3013412531","https://openalex.org/W2951097748","https://openalex.org/W2922502643","https://openalex.org/W2078381694","https://openalex.org/W2066716756","https://openalex.org/W2002642041","https://openalex.org/W1876811344","https://openalex.org/W1544871822"],"abstract_inverted_index":{"We":[0,58,123,147],"introduce":[1],"a":[2,14,52,119],"syntactic":[3],"model":[4],"for":[5],"generating":[6],"sets":[7,90],"of":[8,36,41,54,62,91,114,154],"finite":[9,15,24,34],"and":[10,26,38,99,109,127,138,158],"infinite":[11,28,39,63,72,82,121,131,145],"images":[12],"where":[13],"image":[16,29,46,64,156],"can":[17,48],"be":[18,49,142],"viewed":[19],"as":[20,51,81,104],"an":[21,27,31,71],"array":[22,32],"over":[23],"alphabet":[25],"is":[30,70,79],"with":[33],"number":[35,40],"columns":[37],"rows.":[42],"This":[43],"model,":[44],"called":[45],"grammar,":[47],"considered":[50],"generalization":[53],"classical":[55],"Chromsky":[56],"grammar.":[57],"study":[59,96],"various":[60],"types":[61],"grammars":[65],"using":[66],"Nivat's":[67,126],"derivation":[68],"which":[69,78],"unrestrictive":[73],"derivation,":[74],"Bvichi's":[75],"(respectively":[76,89],"Muller's)":[77],"defined":[80],"derivations":[83],"selected":[84],"by":[85],"some":[86],"repetitive":[87],"set":[88],"rewriting":[92],"rules).":[93],"Then":[94],"we":[95,117,134],"the":[97],"combinatorial":[98],"language":[100],"theoretical":[101],"properties":[102,108],"such":[103],"complexity":[105,115],"measure,":[106],"closure":[107],"decidability":[110],"results.":[111],"In":[112],"terms":[113,153],"measure":[116],"give":[118],"strict":[120],"hierarchy.":[122],"have":[124],"extended":[125,143],"Eilenberg's":[128],"theorems":[129,140],"to":[130,144],"images.":[132,146],"Unfortunately":[133],"prove":[135],"that":[136],"Biichi's":[137],"McNaughton's":[139],"cannot":[141],"also":[148],"characterize":[149],"these":[150],"families":[151],"in":[152],"deterministic":[155],"co-substitution":[157],"\u03c9-languages":[159]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2066716756","counts_by_year":[],"updated_date":"2024-12-17T07:31:26.792836","created_date":"2016-06-24"}