{"id":"https://openalex.org/W2142611800","doi":"https://doi.org/10.1145/1131313.1131320","title":"Ordinary interactive small-step algorithms, I","display_name":"Ordinary interactive small-step algorithms, I","publication_year":2006,"publication_date":"2006-04-01","ids":{"openalex":"https://openalex.org/W2142611800","doi":"https://doi.org/10.1145/1131313.1131320","mag":"2142611800"},"language":"en","primary_location":{"id":"doi:10.1145/1131313.1131320","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1131313.1131320","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","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/A5043571692","display_name":"Andreas Blass","orcid":"https://orcid.org/0000-0001-7445-2980"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andreas Blass","raw_affiliation_strings":["University of Michigan, Ann Arbor, MI"],"affiliations":[{"raw_affiliation_string":"University of Michigan, Ann Arbor, MI","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065430432","display_name":"Yuri Gurevich","orcid":"https://orcid.org/0000-0001-7808-9293"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuri Gurevich","raw_affiliation_strings":["Microsoft Research, Redmond, WA"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, Redmond, WA","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043571692"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":6.4036,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.97139067,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"7","issue":"2","first_page":"363","last_page":"419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9987000226974487,"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/T11567","display_name":"semigroups and automata theory","score":0.9973999857902527,"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/tuple","display_name":"Tuple","score":0.7511874437332153},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6299277544021606},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.579863965511322},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5638843774795532},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5629993081092834},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5544348955154419},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4873407781124115},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.4855892062187195},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4694159924983978},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.41921043395996094},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.4161131978034973},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3464961647987366},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.209669828414917},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.12353411316871643}],"concepts":[{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.7511874437332153},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6299277544021606},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.579863965511322},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5638843774795532},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5629993081092834},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5544348955154419},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4873407781124115},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4855892062187195},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4694159924983978},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.41921043395996094},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.4161131978034973},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3464961647987366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.209669828414917},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.12353411316871643},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1131313.1131320","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1131313.1131320","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.146.2932","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.146.2932","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/en-us/um/people/gurevich/Opera/166.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.146.4229","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.146.4229","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/en-us/um/people/gurevich/Opera/171.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.2.9138","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.9138","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/~gurevich/Opera/166.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W143607683","https://openalex.org/W197061278","https://openalex.org/W1603799276","https://openalex.org/W1853368733","https://openalex.org/W1919452699","https://openalex.org/W1998333922","https://openalex.org/W2113043472","https://openalex.org/W2116445981","https://openalex.org/W2116849571","https://openalex.org/W2117313088","https://openalex.org/W2125522861","https://openalex.org/W2126160338","https://openalex.org/W2134723009","https://openalex.org/W6605851293"],"related_works":["https://openalex.org/W2143551613","https://openalex.org/W4245395944","https://openalex.org/W1979740464","https://openalex.org/W2138823233","https://openalex.org/W2143345456","https://openalex.org/W2023236823","https://openalex.org/W1789991335","https://openalex.org/W2562731034","https://openalex.org/W2499765358","https://openalex.org/W2349728712"],"abstract_inverted_index":{"This":[0],"is":[1],"the":[2,10,40,77,118,125,147,170],"first":[3],"in":[4,56,68,116,145],"a":[5,32,63,91,104,140],"series":[6],"of":[7,47,66,108,120,128,130,142,149,158,162,167,169],"articles":[8],"extending":[9],"abstract":[11,21],"state":[12,22],"machine":[13],"thesis---that":[14],"arbitrary":[15],"algorithms":[16,24,52],"are":[17,154],"behaviorally":[18],"equivalent":[19],"to":[20,85],"machines---to":[23],"that":[25,53,97],"can":[26,80],"interact":[27],"with":[28],"their":[29],"environments":[30],"during":[31],"step":[33,92,98],"rather":[34],"than":[35],"only":[36,62,73],"between":[37],"steps.":[38],"In":[39],"present":[41],"work,":[42],"we":[43,138],"describe,":[44],"by":[45,133],"means":[46],"suitable":[48],"postulates,":[49],"those":[50],"interactive":[51],"(1)":[54],"proceed":[55],"discrete,":[57],"global":[58],"steps;":[59],"(2)":[60],"perform":[61],"bounded":[64],"amount":[65],"work":[67],"each":[69],"step;":[70],"(3)":[71],"use":[72],"such":[74,163],"information":[75],"from":[76,96],"environment":[78],"as":[79,83],"be":[81],"regarded":[82],"answers":[84],"queries;":[86],"and":[87,122,124,151],"(4)":[88],"never":[89],"complete":[90],"until":[93],"all":[94],"queries":[95,121],"have":[99],"been":[100],"answered.We":[101],"indicate":[102],"how":[103],"great":[105],"many":[106],"sorts":[107],"interaction":[109],"meet":[110],"these":[111],"requirements.":[112],"We":[113],"also":[114],"discuss":[115,139],"detail":[117],"structure":[119],"replies":[123],"appropriate":[126],"definition":[127],"equivalence":[129],"algorithms.Finally,":[131],"motivated":[132],"our":[134],"considerations":[135],"concerning":[136],"queries,":[137],"generalization":[141],"first-order":[143],"logic":[144],"which":[146],"arguments":[148],"function":[150],"relation":[152],"symbols":[153],"not":[155],"merely":[156],"tuples":[157,164],"elements":[159],"but":[160],"orbits":[161],"under":[165],"groups":[166],"permutations":[168],"argument":[171],"places.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}