{"id":"https://openalex.org/W4405496230","doi":"https://doi.org/10.3390/e26121105","title":"Enumerating Finitary Processes","display_name":"Enumerating Finitary Processes","publication_year":2024,"publication_date":"2024-12-17","ids":{"openalex":"https://openalex.org/W4405496230","doi":"https://doi.org/10.3390/e26121105","pmid":"https://pubmed.ncbi.nlm.nih.gov/39766734"},"language":"en","primary_location":{"id":"doi:10.3390/e26121105","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26121105","pdf_url":"https://www.mdpi.com/1099-4300/26/12/1105/pdf?version=1734450069","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/26/12/1105/pdf?version=1734450069","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061579980","display_name":"Bridgette Johnson","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin D. Johnson","raw_affiliation_strings":["Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","Mathematics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Mathematics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047565816","display_name":"James P. Crutchfield","orcid":"https://orcid.org/0000-0003-4466-5410"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James P. Crutchfield","raw_affiliation_strings":["Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","Mathematics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA"],"raw_orcid":"https://orcid.org/0000-0003-4466-5410","affiliations":[{"raw_affiliation_string":"Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Mathematics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043648937","display_name":"Christopher J. Ellison","orcid":"https://orcid.org/0000-0002-0393-2941"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher J. Ellison","raw_affiliation_strings":["Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012712469","display_name":"Carl McTague","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Carl S. McTague","raw_affiliation_strings":["DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5047565816"],"corresponding_institution_ids":["https://openalex.org/I84218800"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9843,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80085064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"26","issue":"12","first_page":"1105","last_page":"1105"},"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":0.9994000196456909,"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":0.9993000030517578,"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/finitary","display_name":"Finitary","score":0.9416161775588989},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.6604008674621582},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6403839588165283},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.6219598650932312},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5595989227294922},{"id":"https://openalex.org/keywords/pruning","display_name":"Pruning","score":0.549866259098053},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5240828394889832},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.47157520055770874},{"id":"https://openalex.org/keywords/quantum-finite-automata","display_name":"Quantum finite automata","score":0.4620837867259979},{"id":"https://openalex.org/keywords/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.4530879259109497},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4354391396045685},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4252206087112427},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37858182191848755},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.3530678153038025},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3505403399467468},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2135983109474182}],"concepts":[{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.9416161775588989},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.6604008674621582},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6403839588165283},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.6219598650932312},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5595989227294922},{"id":"https://openalex.org/C108010975","wikidata":"https://www.wikidata.org/wiki/Q500094","display_name":"Pruning","level":2,"score":0.549866259098053},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5240828394889832},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.47157520055770874},{"id":"https://openalex.org/C174327141","wikidata":"https://www.wikidata.org/wiki/Q176837","display_name":"Quantum finite automata","level":4,"score":0.4620837867259979},{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.4530879259109497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4354391396045685},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4252206087112427},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37858182191848755},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.3530678153038025},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3505403399467468},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2135983109474182},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e26121105","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26121105","pdf_url":"https://www.mdpi.com/1099-4300/26/12/1105/pdf?version=1734450069","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:39766734","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39766734","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:escholarship.org:ark:/13030/qt3q19z7t7","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/3q19z7t7","pdf_url":"https://escholarship.org/content/qt3q19z7t7/qt3q19z7t7.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, vol 26, iss 12","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:11675669","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11675669","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11675669/pdf/entropy-26-01105.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:94ae82ca10a34ebb952dcae5d324d81a","is_oa":true,"landing_page_url":"https://doaj.org/article/94ae82ca10a34ebb952dcae5d324d81a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 12, p 1105 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26121105","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26121105","pdf_url":"https://www.mdpi.com/1099-4300/26/12/1105/pdf?version=1734450069","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2146881923","display_name":null,"funder_award_id":"W911NF-12-1-0234","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G3528673648","display_name":null,"funder_award_id":"9060-000709","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4373177538","display_name":null,"funder_award_id":"W911NF-12-1-0234-0","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G81253379","display_name":null,"funder_award_id":"W911NF-12-1-0234-0","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G8905351574","display_name":null,"funder_award_id":"9060-000709","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320312777","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320332815","display_name":"Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405496230.pdf","grobid_xml":"https://content.openalex.org/works/W4405496230.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W22738309","https://openalex.org/W136845799","https://openalex.org/W1585305433","https://openalex.org/W1969958990","https://openalex.org/W2013433986","https://openalex.org/W2046945477","https://openalex.org/W2071458460","https://openalex.org/W2087284982","https://openalex.org/W2090028629","https://openalex.org/W2105594594","https://openalex.org/W2170692333","https://openalex.org/W3104078331","https://openalex.org/W4230164823","https://openalex.org/W6605546954","https://openalex.org/W6719465040"],"related_works":["https://openalex.org/W2950563206","https://openalex.org/W4300232377","https://openalex.org/W1550824632","https://openalex.org/W1975910189","https://openalex.org/W2537940722","https://openalex.org/W4205935260","https://openalex.org/W1594958594","https://openalex.org/W4386400090","https://openalex.org/W2269685284","https://openalex.org/W4297362790"],"abstract_inverted_index":{"We":[0,18],"show":[1],"how":[2],"to":[3,43,56],"efficiently":[4],"enumerate":[5,52],"a":[6,29],"class":[7,41],"of":[8,16,24,45],"finite-memory":[9],"stochastic":[10],"processes":[11],"using":[12],"the":[13,22],"causal":[14],"representation":[15],"\u03f5-machines.":[17,46],"characterize":[19],"\u03f5-machines":[20,54],"in":[21],"language":[23],"automata":[25],"theory":[26],"and":[27,59],"adapt":[28],"recent":[30],"algorithm":[31],"for":[32],"generating":[33],"accessible":[34],"deterministic":[35],"finite":[36],"automata,":[37],"pruning":[38],"this":[39],"over-large":[40],"down":[42],"that":[44],"As":[47],"an":[48],"application,":[49],"we":[50],"exactly":[51],"topological":[53],"up":[55],"eight":[57],"states":[58],"six-letter":[60],"alphabets.":[61]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-29T09:21:14.243279","created_date":"2025-10-10T00:00:00"}