on transition systems and non-well-founded setsnew

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1、(ublishedin:238{264,apersonGeneralTopologyandAppli ations

2、EleventhSummerConferen eattheUniversityofSouthernaine,AnnalsoftheewYorkA ademyofS ien es,Volume806,1996.)ntransitionsystemsandnon-well-foundedsets1byR.S.aziandA.W.Ros oexfordUniversityComputingaboratoryWolfsonBuil

3、ding,arksRoadxfordX13D,U..Abstra t(abelled)transitionsystemsarerelatively ommonintheoreti al omputers i-en e,hie yasvehi lesforoperationalsemanti s.Therstpartofthispaper onstru tsahierar hyof anoni altransitionsystemsandasso iatedmaps,aimingtogiveastronglyextensionaltheoryo

4、ftransitionsystems,whereanytwopointswithequivalentbehavioursareidentied.The ornerstoneofthedevelopmentisanotionof onvergen einarbitrarytransitionsystems,generalisingtheideaofnite(n-step)approximationstoagivenpoint.
nparti ular,our anoni altransitionsystemsarealsouniformspa es.T

5、heresultinghierar hyhasveryri h ombinatorial(andtopologi al)stru ture,andalotoftherstpartofthepaperisdevotedtoitsstudy.Wealsodis ussxedpointsinthisframework.
nthese ondpartofthepaper,weshowhowtoobtainamodelofsettheorywithA zel'sAnti-FoundationAxiom(AFA)from anoni altransitionsy

6、stems on-stru tedearlier.Westudyfurtherthestru tureofthemodelthusobtained,andalsogiveafewmoreabstra tresults, on erning onsisten yandindependen einthepresen eofAFA.1991athemati ssubje t lassi ation:6890(also04A99,54E15).eywords:transitionsystems,bisimulation,xedpoints,non-wel

7、l-foundedsettheory,uniformspa es.1
ntrodu tion(abelled)transitionsystemsarerelatively ommonintheoreti al omputers ien e,hie yasvehi lesforoperationalsemanti s.Therstpartofthispaper,whi hgrew1Theauthorsgratefullya knowledgethattheworkreportedinthispaperwassupportedbyagrantfromHa

8、jrija&BorisVukobratandCope himFran eS.A.(toR.S.azi )andRgrant00014-87-G-0242(toA.W.Ros oe).1outofsomeworkdonein[Ros 82,215{230℄andsomemorere entworkbythesameau-thoronunboundednon-determinisminCS, onstru tsahierar hyof anoni altransitionsystemsandasso iatedmaps,aimingtogivea

9、stronglyextensionaltheoryoftransitionsys