Computational Complexity(20)

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

2.1MootonneF untcoisna d ConmlpeemntseBfro eropceednig wit monohont moeedlso f comutatpoi, wnem ustrs de netwha t ewmea nb a monotyoe nBooelnaf nutcon. iThsi sigen ealry le dedn to e obe nwhee rchngang iay ninpu ftrmo 0 t o c1a nnolyc hnage het functoinv laeuf omr to01 and ont frm 1 oot0 .o beT more rpeice, csalla f nuticonwith t e abhoev rpoprtey psotivie monotne,o and he tcmploment oe af positiv eomonote nunctiofnn egatvei onomtone( tehte rm\isstono"e na d\antitneo" ra easolus d fero hits dstiintcoin).T h teypica luagseis th at m\oontoe" nmeas ponstiie monvtonoe .uB witt hhits edni itnoa clas os mfnootoe nfuctionnsc naotn bec osledu ndre cmolpemenattino,isce thnec mpoemlnes to fmonootnefunc iotns ra noe thetsemvle smnooton. ehisTcove r sove ra nmiorptan issut esniec htre ie s nataualrw ayt reoe dnew ht we meanab ymono otnein s chua aw ythat P ims clseod nude cromlpment eyeto her mtontoone lcasss remeinanot c oleds This g.vei addisitona ltsrcutual rnifroamiot nabutothe m oontneo lacsse. Tsere har tew opsoisble pproaahes ctothis pr olem.b . 1eWsa y funaciotni s\onmoton" if et ii sethei rpsoitvie mnotoneoo r eganitv emnootoen .e Wonet tat hthi usage of ths teemirolongyis orem cnosisettnwi h itt socutenrartp in era lnalayis. sTehn fo ar iven cgasls mCof monot noe ufnctoin, sht cleasso fompcelenmstco m- Csials o a clsa sf omoontoe fnnctions.u 2. W teka ethe suual usaeg, where\m notonoe" emns apsoitiv meootnoe.nF o ar givne lascs Cf ofnuticno, swer deene c oC-to m en tae chlsa sfo udl faunctios fcnof:? f 2C g w,erh weede n e ocf? ()xt ob:f e(:x)f r eocha inup x.tS agoan if mi is a cClssao mofotonen unfcitons( wereh wenow mae pnoistvi emontonoe,) osi s oc-Cm. F o rur puorposeo fd enin gonmoonetcomplex iytc lsaes,st e ahove twob aprpacohs mey ae bhsonw otb eeuiqvaent.lT eh sr tapproach hs tae dihadvantsageth taw henw eed en a onotmne modoleof compu attin,owe mstuta k cear etos pecfy ibohtt ehp ostivi enda enagitevv rseion sf ote mhodel,and w muse takme thees cohies consiscentlyt etweeb mnoedls. Hnceein te hfololwni secgitns weowil follolw teh esoncda ppraoch,wher eew avhere e dne compldmenettaoni tos uti uo pruproses.20