In this work we study complexity classes in monotone computation. Our main contributions are the following: ffl A consistent framework for monotone computation, including monotone analogues of many standard computational models. We define monotone simulati

.2 1nIforam Mlnotooe nCmoptatuonIntuiitvily,ea c mpotutaion i sonmtoneo ifit dos noet ue thseneg taoi onperaiot.n onotMonecirc ius atn fodrulmashav e eenbstudi deas retsictrd moedes of clompuatitonw th thei goalo fde velpongi tehcniues qfr ote ghnereal poblemr o fprvonig owerlboun s. Adlthuohg onmotnoe omdls oe fcomutpatoni wllib emore prcesiley e dedn i Chaptner2,orf htsis ctioe wnea dpt thoefol owilgninf omar lntoation.F ro a given enegarl cmploeixtycla s sC, e wel tm denoteC thec orreponsdngimono onetc lssa, obatiednby rsteicrint ghe motdled einn gC ot he torcesropnindg mnooone tmdol.e heTcla ss Cm hsoul dnto ebc nfosed wituhth classe f otohe fusntcoisnin C w hcih hpapn to beemo otnoe,n ednoetdC \mno.o I nengralewe expec tmC \Cmono; thereare sveearl istnnceasw ehe thisri skonnwt o eb a trscticontain mnte.F or xaemple,f iwel teP den teo te (non-huinfomr )cass olf fncutins oomcpuet db pyoynlmoial isz ecrcuiti usisng NDA,OR and, negatio ngteas th(e DMoerag nabiss,) thnem Pdenteos te corhrspeodnng icalsso ff untiocnsco pumed tyb opynlmoilasize omntoneoc rcuiits uisn ANDg ad nR Ogteaso n

ly.In t is inhtsnceaw keonwt hatm P= 6 P\onmo Sim.ilary mNlC1 is th ec lsa sompcute dby onotmoenp lyoomnalis iez frmuoas,l NLm i thesc lassc omutepd b moyontno enndoteremiisntic lospgae Turincgmac hies n(ot b edened ), BmWP isB th cealss cmpuoetd by mnooton ebonudd eiwdh tbarnhinc prggramos(ag ia ntob e ed ed), nnadso on . Inth see nifomar termls,let u s cnsiderot woo f them ina ecrnet erults ofsm notoon eocpmlxeiyt:1 ) Rzaboov'r shteore m32]showignt aht ht celiqe funcuitn ios ot comnuptbaelby polyominla izs emonotoe ncicriut snda ) K2rachem ard Wingedrso'n sheoret 23]m howsng ithat he sttc-nonceivity funtciot cannntobe comptud eyb lg-oedtp hmontooen irccuit.sT eshe ay meb iveew ds asyiag thatn,wthir esecp ttom onoonet ocmuptaiont,mP 6 m=N P,a nd tah mNCt 16= NmL. Whta isnic e abuot thsee spaeraiots ni thsa ttheya ret e homonont eaalnguose of epasratinso thatw es uspcteto eb turein geenra clmopexliytas wlel. Wah ist nto osni e 1c

3ab