{"id":"https://openalex.org/W2172117229","doi":"https://doi.org/10.3233/fi-2015-1198","title":"Semilinear Sets and Counter Machines: a Brief Survey","display_name":"Semilinear Sets and Counter Machines: a Brief Survey","publication_year":2015,"publication_date":"2015-06-01","ids":{"openalex":"https://openalex.org/W2172117229","doi":"https://doi.org/10.3233/fi-2015-1198","mag":"2172117229"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2015-1198","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2015-1198","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","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/A5110211208","display_name":"\u00d3scar H. Ibarra","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Oscar H. Ibarra","raw_affiliation_strings":["Department of Computer Science, University of California, Santa Barbara, CA 93106, USA. ibarra@cs.ucsb.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California, Santa Barbara, CA 93106, USA. ibarra@cs.ucsb.edu","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002387043","display_name":"Shinnosuke Seki","orcid":"https://orcid.org/0000-0002-0276-3322"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]},{"id":"https://openalex.org/I32943570","display_name":"Helsinki Institute for Information Technology","ror":"https://ror.org/05kph4940","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I32943570","https://openalex.org/I9927081"]},{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI","US"],"is_corresponding":false,"raw_author_name":"Shinnosuke Seki","raw_affiliation_strings":["Department of Computer Science, University of California, Santa Barbara, CA 93106, USA. ibarra@cs.ucsb.edu","Helsinki Institute for Information Technology (HIIT), Department of Information and Computer Science, Aalto University, P. O. Box 15400, FI-00076, Aalto, Finland. shinnosuke.seki@aalto.fi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California, Santa Barbara, CA 93106, USA. ibarra@cs.ucsb.edu","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Helsinki Institute for Information Technology (HIIT), Department of Information and Computer Science, Aalto University, P. O. Box 15400, FI-00076, Aalto, Finland. shinnosuke.seki@aalto.fi","institution_ids":["https://openalex.org/I32943570","https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3529,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66009611,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"138","issue":"1-2","first_page":"61","last_page":"76"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.994700014591217,"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":0.9900000095367432,"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/counterexample","display_name":"Counterexample","score":0.5754207372665405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.461967408657074},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3659061789512634},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3345412611961365},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.280031681060791}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.5754207372665405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.461967408657074},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3659061789512634},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3345412611961365},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.280031681060791}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2015-1198","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2015-1198","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4816937414","display_name":"Mathematical model of cotranscriptional folding and its Turing universality","funder_award_id":"15H06212","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W125092026","https://openalex.org/W147131300","https://openalex.org/W300949053","https://openalex.org/W1497287285","https://openalex.org/W1513287292","https://openalex.org/W1580526823","https://openalex.org/W1580879785","https://openalex.org/W1589381382","https://openalex.org/W1598043785","https://openalex.org/W1599939219","https://openalex.org/W1614820560","https://openalex.org/W1630184508","https://openalex.org/W1646814793","https://openalex.org/W1694069253","https://openalex.org/W1964431911","https://openalex.org/W1974451646","https://openalex.org/W1975359072","https://openalex.org/W1979876920","https://openalex.org/W1988472308","https://openalex.org/W1988946128","https://openalex.org/W1991034910","https://openalex.org/W2000118875","https://openalex.org/W2002089154","https://openalex.org/W2004459113","https://openalex.org/W2006301099","https://openalex.org/W2019146106","https://openalex.org/W2023042027","https://openalex.org/W2023999667","https://openalex.org/W2035314514","https://openalex.org/W2037124586","https://openalex.org/W2050162072","https://openalex.org/W2050207280","https://openalex.org/W2050310895","https://openalex.org/W2053402117","https://openalex.org/W2054743028","https://openalex.org/W2057559629","https://openalex.org/W2065105492","https://openalex.org/W2076858908","https://openalex.org/W2077804036","https://openalex.org/W2080640642","https://openalex.org/W2080700991","https://openalex.org/W2082899028","https://openalex.org/W2084335565","https://openalex.org/W2089107726","https://openalex.org/W2090766691","https://openalex.org/W2092008211","https://openalex.org/W2096801634","https://openalex.org/W2102924625","https://openalex.org/W2121428680","https://openalex.org/W2134468631","https://openalex.org/W2156308118","https://openalex.org/W2157390113","https://openalex.org/W2162593546","https://openalex.org/W2183075714","https://openalex.org/W2326418800","https://openalex.org/W2338160616","https://openalex.org/W2358436021","https://openalex.org/W2383021692","https://openalex.org/W2620826411","https://openalex.org/W2955442659","https://openalex.org/W2958814800","https://openalex.org/W4235577069","https://openalex.org/W4243967634","https://openalex.org/W4246319563","https://openalex.org/W4254397836","https://openalex.org/W4285719527","https://openalex.org/W4392206348"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W3204670144","https://openalex.org/W2163101548","https://openalex.org/W1988934358","https://openalex.org/W2587222766","https://openalex.org/W4387718369","https://openalex.org/W3014450817"],"abstract_inverted_index":{"Semilinear":[0],"sets":[1,116],"are":[2],"one":[3,135],"of":[4,21,28,55,60,94,109,119,129,140],"the":[5,16,19,52,92,127,138],"most":[6],"important":[7],"concepts":[8],"in":[9,117,137],"theoretical":[10],"computer":[11],"science,":[12],"as":[13,42,64],"illustrated":[14],"by":[15],"fact":[17],"that":[18,97,113],"set":[20,41,67],"nonnegative":[22],"integer":[23],"solutions":[24],"to":[25,37,90],"any":[26,39],"system":[27],"Diophantine":[29],"equations":[30],"is":[31],"semilinear.":[32],"Parikh's":[33,88],"theorem":[34,89],"enables":[35],"us":[36],"represent":[38,99],"semilinear":[40,62,100,115],"a":[43,61,65,69,73,106,110,131,141],"pushdown":[44],"automaton":[45,71],"(PDA).":[46],"We":[47,76,86,124],"summarize":[48],"recent":[49],"results":[50],"on":[51,146],"descriptional":[53],"complexity":[54],"conversions":[56],"among":[57],"different":[58],"representations":[59],"set:":[63],"vector":[66],"(conventional),":[68],"finite":[70],"(FA),":[72],"PDA,":[74],"etc..":[75],"also":[77],"discuss":[78],"semilinearity-preserving":[79],"operations":[80],"like":[81],"union,":[82],"intersection,":[83],"and":[84],"complement.":[85],"use":[87],"enlarge":[91],"class":[93],"finite-state":[95],"machines":[96,120],"can":[98],"sets.":[101],"In":[102],"particular,":[103],"we":[104],"give":[105],"simpler":[107],"proof":[108],"known":[111],"result":[112],"characterizes":[114],"terms":[118],"with":[121,133],"reversal-bounded":[122],"counters.":[123],"then":[125],"investigate":[126],"power":[128],"such":[130],"machine":[132],"only":[134],"counter":[136],"context":[139],"long-standing":[142],"conjecture":[143],"about":[144],"repetition":[145],"words.":[147]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}