{"id":"https://openalex.org/W2911336923","doi":"https://doi.org/10.1142/s0218196719500255","title":"Algebraic properties of <tt>if-then-else</tt> and commutative three-valued tests","display_name":"Algebraic properties of <tt>if-then-else</tt> and commutative three-valued tests","publication_year":2019,"publication_date":"2019-01-25","ids":{"openalex":"https://openalex.org/W2911336923","doi":"https://doi.org/10.1142/s0218196719500255","mag":"2911336923"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196719500255","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196719500255","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5067874082","display_name":"Kh\u00ed-U\u00ed Soo","orcid":null},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Kh\u00ed-U\u00ed Soo","raw_affiliation_strings":["Department of Computer Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027252348","display_name":"Tim Stokes","orcid":"https://orcid.org/0000-0003-2908-8563"},"institutions":[{"id":"https://openalex.org/I52179390","display_name":"University of Waikato","ror":"https://ror.org/013fsnh78","country_code":"NZ","type":"education","lineage":["https://openalex.org/I52179390"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Tim Stokes","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Waikato, Private Bag 3105, Hamilton, 3240, New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Waikato, Private Bag 3105, Hamilton, 3240, New Zealand","institution_ids":["https://openalex.org/I52179390"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067874082"],"corresponding_institution_ids":["https://openalex.org/I154130895"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03167212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"04","first_page":"743","last_page":"759"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","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/T11567","display_name":"semigroups and automata theory","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/T11727","display_name":"Advanced Algebra and Logic","score":0.9998000264167786,"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":0.9995999932289124,"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/mathematics","display_name":"Mathematics","score":0.5934028625488281},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5052421689033508},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4972842037677765},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4770214557647705},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4698561429977417},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.466399610042572},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4320395290851593},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.413411945104599},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.27477726340293884},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24035823345184326},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22840145230293274}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5934028625488281},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5052421689033508},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4972842037677765},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4770214557647705},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4698561429977417},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.466399610042572},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4320395290851593},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.413411945104599},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.27477726340293884},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24035823345184326},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22840145230293274},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196719500255","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196719500255","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:researchcommons.waikato.ac.nz:10289/12567","is_oa":false,"landing_page_url":"https://hdl.handle.net/10289/12567","pdf_url":null,"source":{"id":"https://openalex.org/S4306400944","display_name":"Research Commons (University of Waikato)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I52179390","host_organization_name":"University of Waikato","host_organization_lineage":["https://openalex.org/I52179390"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1965089427","https://openalex.org/W1972401918","https://openalex.org/W1986418951","https://openalex.org/W1998368317","https://openalex.org/W2010342693","https://openalex.org/W2036869460","https://openalex.org/W2055563322","https://openalex.org/W2064576648","https://openalex.org/W2068047345","https://openalex.org/W2084792518","https://openalex.org/W2093397547","https://openalex.org/W2121190750","https://openalex.org/W2161472487","https://openalex.org/W2166089338","https://openalex.org/W2963043115","https://openalex.org/W2963084075"],"related_works":["https://openalex.org/W2361805396","https://openalex.org/W2972254340","https://openalex.org/W2022231341","https://openalex.org/W1805912688","https://openalex.org/W4255476312","https://openalex.org/W2373973507","https://openalex.org/W4250902763","https://openalex.org/W2351154965","https://openalex.org/W2357579988","https://openalex.org/W2041503010"],"abstract_inverted_index":{"This":[0],"paper":[1],"establishes":[2],"a":[3,20,123],"finite":[4],"axiomatization":[5],"of":[6,108,138,162],"possibly":[7,157],"non-halting":[8],"computer":[9],"programs":[10,28,39,48,118],"and":[11,29,42,44,50,97,110,126,143],"tests,":[12],"with":[13,23,69],"the":[14,27,30,33,47,82,85,105,111,159,163,167,177,206],"if-then-else":[15],"operation.":[16],"The":[17,35,79,129],"model":[18,171],"is":[19,40,104,120,202],"two-sorted":[21],"algebra,":[22],"one":[24],"sort":[25],"being":[26,32],"other":[31,207],"tests.":[34],"main":[36],"operation":[37,107,113,131],"on":[38,62,75,81,117],"composition,":[41],"1":[43],"0":[45],"represent":[46],"skip":[49],"loop":[51],"(i.e.":[52],"never":[53],"halts)":[54],"respectively.":[55],"Programs":[56],"are":[57,84,153],"modeled":[58,71],"as":[59,72,174,191],"partial":[60,73],"functions":[61],"some":[63],"state":[64],"space":[65],"[Formula:":[66,76,91,94,98,114,132,140,188,195,199],"see":[67,77,92,95,99,115,133,141,189,196,200],"text],":[68,93],"tests":[70,83,152],"predicates":[74],"text].":[78,100],"operations":[80,137],"usual":[86],"logical":[87,164],"connectives":[88,165],"\u2227,":[89],"\u2228,":[90],"text]":[96,116,134,142,190,197,201],"In":[101],"addition,":[102],"there":[103],"hybrid":[106],"if-then-else,":[109],"test-valued":[112],"which":[119],"true":[121],"when":[122],"program":[124],"halts,":[125],"undefined":[127],"otherwise.":[128],"halting":[130],"implies":[135],"that":[136],"domain":[139,144],"join":[145],"\u2228":[146],"may":[147],"also":[148],"be":[149,156],"expressed.":[150],"When":[151],"assumed":[154],"to":[155,176],"non-halting,":[158],"evaluation":[160,182],"strategy":[161],"affects":[166],"result.":[168],"Here":[169],"we":[170,186],"parallel":[172],"evaluation,":[173],"opposed":[175],"common":[178],"sequential":[179],"(or":[180],"short-circuit)":[181],"strategy.":[183],"For":[184],"example,":[185],"view":[187],"false":[192],"if":[193,205],"either":[194],"or":[198],"false,":[203],"even":[204],"does":[208],"not":[209],"halt.":[210]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}