?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=On+Star+Expressions+and+Completeness+Theorems&rft.creator=Schmid%2C+T&rft.creator=Rot%2C+J&rft.creator=Silva%2C+A&rft.description=An+open+problem+posed+by+Milner+asks+for+a+proof+that+a+certain+axiomatisation%2C+which+Milner+showed+is+sound+with+respect+to+bisimilarity+for+regular+expressions%2C+is+also+complete.+One+of+the+main+difficulties+of+the+problem+is+the+lack+of+a+full+Kleene+theorem%2C+since+there+are+automata+that+can+not+be+specified%2C+up+to+bisimilarity%2C+by+an+expression.+Grabmayer+and+Fokkink+(2020)+characterise+those+automata+that+can+be+expressed+by+regular+expressions+without+the+constant+1%2C+and+use+this+characterisation+to+give+a+positive+answer+to+Milner's+question+for+this+subset+of+expressions.+In+this+paper%2C+we+analyse+Grabmayer+and+Fokkink's+proof+of+completeness+from+the+perspective+of+universal+coalgebra%2C+and+thereby+give+an+abstract+account+of+their+proof+method.+We+then+compare+this+proof+method+to+another+approach+to+completeness+proofs+from+coalgebraic+language+theory.+This+culminates+in+two+abstract+proof+methods+for+completeness%2C+what+we+call+the+local+and+global+approaches%2C+and+a+description+of+when+one+method+can+be+used+in+place+of+the+other.&rft.subject=Regular+expressions%2C+bisimulation%2C+program+semantics%2C+coalgebra.&rft.date=2021-12&rft.type=Proceedings+paper&rft.language=eng&rft.source=+++++In%3A++Proceedings%3A+37th+Conference+on+Mathematical+Foundations+of+Programming+Semantics.++(pp.+pp.+242-259).+++(2021)+++++&rft.format=text&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10130031%2F7%2FSilva_2106.08074v2.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10130031%2F&rft.rights=open