{"id":"https://openalex.org/W2397464784","doi":"https://doi.org/10.25596/jalc-2010-121","title":"Nondeterministic State Complexity of Positional Addition","display_name":"Nondeterministic State Complexity of Positional Addition","publication_year":2009,"publication_date":"2009-07-29","ids":{"openalex":"https://openalex.org/W2397464784","doi":"https://doi.org/10.25596/jalc-2010-121","mag":"2397464784"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.313.8395","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.313.8395","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0907.5072v1.pdf","raw_type":"text"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.0907.5072","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012840795","display_name":"Galina Jir\u00e1skov\u00e1","orcid":"https://orcid.org/0000-0001-9817-8197"},"institutions":[{"id":"https://openalex.org/I207624831","display_name":"Slovak Academy of Sciences","ror":"https://ror.org/03h7qq074","country_code":"SK","type":"government","lineage":["https://openalex.org/I207624831"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Jiraskov\u00e1, Galina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5005683089","display_name":"Alexander Okhotin","orcid":"https://orcid.org/0000-0002-1615-2725"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Okhotin, Alexander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"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/T11567","display_name":"semigroups and automata theory","score":0.9991000294685364,"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":0.9991000294685364,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9968000054359436,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9937000274658203,"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/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.8789000511169434},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.6571996808052063},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6109273433685303},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5668675303459167},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.534774124622345},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.510478138923645},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.48545581102371216},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4420090913772583},{"id":"https://openalex.org/keywords/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.42786356806755066},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4197959303855896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3577134609222412},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2823981046676636},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.2578326165676117},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19931623339653015},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.18339571356773376}],"concepts":[{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.8789000511169434},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.6571996808052063},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6109273433685303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5668675303459167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.534774124622345},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.510478138923645},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.48545581102371216},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4420090913772583},{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.42786356806755066},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4197959303855896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3577134609222412},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2823981046676636},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.2578326165676117},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19931623339653015},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.18339571356773376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.313.8395","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.313.8395","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0907.5072v1.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.0907.5072","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0907.5072","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.25596/jalc-2010-121","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2010-121","pdf_url":null,"source":null,"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:10.48550/arxiv.0907.5072","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0907.5072","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2095269027","https://openalex.org/W1577889095","https://openalex.org/W2028786042","https://openalex.org/W1972285175","https://openalex.org/W1884045513","https://openalex.org/W1966076725","https://openalex.org/W2071780227","https://openalex.org/W153129168","https://openalex.org/W647462584","https://openalex.org/W1977834963","https://openalex.org/W1069688093","https://openalex.org/W2756180352","https://openalex.org/W2787306511","https://openalex.org/W1511430947","https://openalex.org/W2887759255","https://openalex.org/W2747875137","https://openalex.org/W2058773739","https://openalex.org/W1531148340","https://openalex.org/W2963979500","https://openalex.org/W61785131"],"abstract_inverted_index":{"Consider":[0],"nondeterministic":[1,36,58],"finite":[2],"automata":[3,37],"recognizing":[4],"base-k":[5],"positional":[6],"notation":[7],"of":[8,28,38,66],"numbers.":[9],"Assume":[10],"that":[11,24],"numbers":[12,29],"are":[13,33],"read":[14],"starting":[15],"from":[16],"their":[17,45],"least":[18],"significant":[19],"digits.":[20],"It":[21],"is":[22,54,68],"proved":[23],"if":[25],"two":[26],"sets":[27],"S":[30],"and":[31,40],"T":[32],"represented":[34,55],"by":[35,56],"m":[39],"n":[41],"states,":[42],"respectively,":[43],"then":[44],"sum":[46],"$\\{s":[47],"+t":[48],"\\mid":[49],"s\\in":[50],"S,":[51],"t\\in":[52],"T\\}$":[53],"a":[57],"automaton":[59],"with":[60],"$2mn+2m+2n+1$":[61],"states.":[62],"Moreover,":[63],"this":[64],"number":[65],"states":[67],"in":[69],"the":[70],"worst":[71],"case":[72],"necessary":[73],"for":[74],"all":[75],"$k":[76],"\\geq":[77],"6$.":[78]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}