digraph G{ np->zero1npc; sharpac0->gapac0; sharpl->det; l->parityl; nldivpoly->parityldivpoly; logcfl->paritysac1; qma->a0pp; awpp->a0pp; coceqp->a0pp; a0pp->pp; nc0->ac0; ac0->qac0; ac0->mac0; ac0m->nc1; acc0->tc0; kpbp->acc0; szk->am; am->pi2p; am->npdivpoly; maexp->amdashexp; amdashexp->eh; amdashexp->s2exppnp; ampmp->mp2; ap2->re; app2->pp; awpp->app2; ptas->apx; ganspace->aucspace; aucspace->yacc; bqp->awpp; wapp->awpp; wpp->awpp; awstar->awsat; awsat->awp; awt->awstar; bh->delta2p; rhspace->bphspace; bpl->sc; bpl->pl; bppdashobdd->bqpdashobdd; nl->nlog; fewp->np; p->pnpk; pnplog->bpppath; bpppath->pp; rspace->bpspace; bphspace->bpspace; bqpdivlog->bqpdivqlog; bqpdivqlog->bqpdivpoly; bqp->bqpdivqlog; bqpdivpoly->bqpdivqpoly; bqpdivqpoly->ppdivpoly; cfl->logcfl; ch->npspace; clog->cp; npc->compnp; conexp->nexpdivpoly; cp->cnp; pzk->czk; szk->czk; det->nc2; nl->det; pl->det; szk->dqp; bqp->dqp; dqp->pp; np->fnp; ee->eexp; ee->nee; eexp->neexp; cone->nedivpoly; eh->seh; elementary->pr; fptas->eptas; eptas->ptas; np->existsbpp; existsbpp->ma; np->existsniszk; niszk->existsniszk; bqpdivqpoly->expdivpoly; fewp->few; few->spp; fnldivpoly->sharpldivpoly; tfnp->fnp; ac0->foll; foll->ac; fpt->fptnu; fpt->w1; fpt->fpr; fptas->fpt; fptsu->fpt; compip->frip; check->frip; p->ga; ga->gi; npspace->ganspace; bpspace->ganspace; gi->np; gi->szk; pdivlog->iclogpoly; iclogpoly->pdivpoly; nc1->l; l->nl; l->pbp; l->rl l->modkl; logsnp->lognp; lognp->betap; logsnp->qp; lwpp->wpp; gi->lwpp; ma->sigma2pinterpi2p; mac0->tc0; maxpb->maxnp; xormipstar21->mipstar21; mnc1->ml; ml->mp; ml->mnl; ml->mconl; mtc0->mnc1; mp->mnp; gi->modkp; modpp->modp; modp->ampmp; modzkl->modkl; modzkl->nl; logfewnl->modzkl; tc0->nc1; ne->nexp; nee->neexp; niszk->niszkh; niszkh->szk; nl->nldivpoly; nldivpoly->logcfl; nlog->p; npc->np; npcc->phcc; npsv->npmv; npmvt->npmv; apx->npo; npopb->npo; npsvt->npsv; npsvt->npmvt; ac->p; sc->p; bpp->pdivpoly; psharpp->npspace; psharpp1->psharpp; ppdashparityp->psharpp1; pdashobdd->pbp; kpbp->eqbp; pcc->npcc; pcc->bppcc; pcd->gpcd; bpp->ph; phi2p->sigma2p; phi2p->pi2p; pinc->pio; npspace->pk; pnpk->pnplog; pdashobdd->bppdashobdd; ppa->tfnp; ppad->ppa; ppad->ppads; ppads->ppp; ppp->tfnp; rp->promiserp; promiserp->promisebpp; pl1->pt1; plinfinity->pt1; pzk->szk; qam->qip2; qam->npspace; ma->qcma; qcma->qma; qip->exp; npspace->qip; qnc0->qncf0; qncf0->qacc0; qszk->npspace; pr->r; reg->nc1; rhl->rl; rl->sc2; sc2->sc; rnc->bqnc; rspace->nspace; ma->s2p; delta2p->s2p; ma->sbp; wapp->sbp; sbp->am; sbp->bpppath; tally->sparse; ul->spl; spl->ceql; spl->modkl; spp->ceqp; spp->wpp; gi->spp; szk->amintercoam; amintercoam->am; amintercoam->coam; npo->fp; p->fp; gapac0->p; fptas->p; szk->qszk; pls->tfnp; bpp->treebqp; treebqp->bqp; up->uap; uap->spp; ucc->l; conp->us; ceqp->pp; npinterus->us; us->ceqp; npinterus->np; np->cous; vp->vnp; vp->vqp; vnc->vp; wsat->wp; wt->wsat; wt->wstart; wt->wstar; xormipstar21->exp; xpuniform->xp; fpt->xp; check->nexpinterconexp; e->exp; p->e; e->ne; exp->nexp; nc2->ac; p->zpp; zpp->rp; zpp->corp; rp->bpp; corp->bpp; e->ee; r->re; nexp->conexp; np->ph; rp->np; fp->sharpp; fl->sharpl; sharpp->fpspace; maxsnp->fpt; espace->expspace; npspace->espace; bpp->promisebpp; bqp->promisebqp; p->promisep; promisep->promiserp; modkp->ampmp; sharpp->fpttmodp; ceqp->pcttmodp; np->ne; npbpp->zppnp; npbpp [label="NP^BPP"]; zppnp [label="ZPP^NP,ZPP^NP^BPP"]; bppparityp->psharpp1; ph->bppparityp; bppparityp [label="BPP^+P"]; spp->parityp; parityp->pp; pp->psharpp; p->pdashsel; pdivquadratic->pdivpoly; pdashsel->npdivlinearinterconpdivlinear; npdivlinearinterconpdivlinear [label="NP/linear inersect coNP/linear"]; bpe->bpee; ntime->nspace; zpp->zpe; zpe->zptime; ue->ne; subexp->exp; snp->np; logcfl->sac; rpp->np; npspace->qpspace; qpspace->expspace; e->bpe; ocq->bqp; logsnp->np; qnc0->qnc1; p->qp; qp->subexp; subexp->e; pcttmodp [label="P_{ctt}^{ModP}"]; pttsharpp [label="P_{tt}^{#P},P_{tt}^{ModP},P_{tt}^{AmpMP},P_{tt}^{MP}"]; fpttmodp [label="FP_{tt}^{ModP}"]; modpp[label="Mod_p P"]; fpspace [label="FPSPACE"]; fl [label="FL"]; zptime [label="ZPTIME(f(n))"]; zpp [label="ZPP, RP intersect coRP"]; zpe [label="ZPE"]; xpuniform [label="XP_uniform, SP"]; xp [label="XP"]; xormipstar21 [label="XOR-MIP*[2,1]"]; wstart [label="W^* -[t]"]; wt [label="W[t]"]; wstar [label="W[*]"]; wsat [label="W[SAT]"]; wpp [label="WPP"]; wp [label="W[p]"]; wapp [label="WAPP"]; w1 [label="W[1]"]; vqp [label="VQP_k"]; vp [label="VP_k"]; vnp [label="VNP_k"]; us [label="US"]; ue [label="UE"]; ucc [label="UCC"]; uap [label="UAP"]; up [label="UP"]; treeregular [label="TREE-REGULAR"]; treeregular->reg; treebqp [label="TreeBQP"]; tfnp [label="TFNP"]; tc0 [label="TC^0"]; tally [label="TALLY"]; subexp [label="SUBEXP"]; spp [label="SPP"]; spl [label="SPL"]; sparse [label="SPARSE"]; spanp [label="span-P"]; sharpp->spanp; sp2 [label="SP"]; sp2->p; snp [label="SNP"]; slicewisepspace [label="SLICEWISE PSPACE"]; skc [label="SKC"]; sigma2p [label="\Sigma_2 P"]; sfk [label="SF_k"]; npspace->sfk; selfnp [label="SelfNP"]; selfnp->np; seh [label="SEH"]; sbp [label="SBP"]; sac0 [label="SAC^0"]; sac0->logcfl; sac [label="SAC"]; s2exppnp [label="S_2 -EXP*P^NP"]; s2p [label="S_2 P, symP"]; rpp [label="RPP"]; rnc [label="RNC"]; rhl [label="R_H L"]; rspace [label="RSPACE"]; reg [label="REG"]; re [label="RE"]; r [label="R"]; qszk [label="QSZK"]; qpspace [label="QPSPACE"]; qp [label="QP"]; qnc1 [label="QNC^1"]; qncf0 [label="QNC_f^0"]; qnc0 [label="QNC^0"]; qmiple [label="QMIP_le"]; qmiple->nexp; qmip [label="QMIP"]; qma2 [label="QMA(2)"]; qip2 [label="QIP(2)"]; qh [label="QH"]; qcma [label="QCMA"]; qcfl [label="QCFL"]; qam [label="QAM"]; qacc0 [label="QACC^0"]; qac0 [label="QAC^0 [m]"]; qac0 [label="QAC^0"]; pzk [label="PZK"]; ptdivwk [label="PT/WK(f(n),g(n))"]; ac->ptdivwk; ptas [label="PTAS"]; pt1 [label="PT_1"]; pdashsel [label="P-sel"]; pdashsel->pdivquadratic; prspace [label="PrSPACE(f(n)), Pr_H SPACE(f(n))"]; promiserp [label="PromiseRP"]; promisep [label="PromiseP"]; promisebqp [label="PromiseBQP"]; promisebpp [label="PromiseBPP"]; pdashr [label="P_R"]; pr [label="PR"]; ppdashparityp [label="PP^+P"]; polyl [label="polyL"]; polyl->eespace; pnplog [label="P^NP[log], \Theta_2 P"]; pnpk [label="P^NP[k]"]; pls [label="PLS"]; pll [label="PLL"]; pll->tfnp; pl1 [label="PL_1"]; pkc [label="PKC"]; pzk->pkc; pk [label="P^K"]; pio [label="PIO"]; pinc [label="PINC"]; pinc->yacc; pi2p [label="\pi_2 P"]; phi2p [label="\phi_2 P"]; phcc [label="PH^CC"]; ph [label="PH"]; pfchk [label="PFCHK(t(n))"]; pf [label="PF"]; pexp [label="PEXP"]; pexp->nexp; permup [label="PermUP"]; permup->up; p->permup; pcp [label="PCP(r(n),q(n))"]; pclose [label="P-close"]; p->pclose; pcd [label="PCD(r(n),q(n))"]; pcc [label="P^CC"]; pdivquadratic [label="P/quadratic"]; pdashc [label="P_C"]; kpbp [label="k-PBP"]; pac0 [label="PAC^0"]; psharpp1 [label="P^#P[1]"]; optp [label="OptP"]; optp->spanp; ocq [label="OCQ"]; ntime [label="NTIME(f(n))"]; dtime->ntime; nt [label="NT"]; nt->yacc; npsvtsel [label="NPSV_t -sel"]; npsvtsel->yacc; npsvt [label="NPSV_t"]; npsvsel [label="NPSV-sel"]; npsvsel->npsvselinternp; np->npsvselinternp; npsvselinternp [label="NPSV-sel intersect NP"]; npsvselinternp->npinterconpdivpoly; npinterconpdivpoly [label="(NP intersect coNP)/poly)"]; npsvsel->npdivpolyinterconpdivpoly; npdivpolyinterconpdivpoly [label="NP/poly intersect coNP/poly"]; eptsel->expdivlinear; eptsel [label="E_T^{p}(P-sel)"]; expdivlinear [label="EXP/linear"]; expdivlinear->expdivpoly; npsvsel->yacc; npsv [label="NPSV"]; npdashr [label="NP_R"]; pdashr->npdashr; npdashr->npdashc; nppsamp [label="(NP,P-samplable)"]; nppsamp->yacc; npopb [label="NPOPB"]; npo [label="NPO"]; npmvtsel [label="NPMV_t -sel"]; npmvtsel->yacc; npmvt [label="NPMV_t"]; npmvsel [label="NPMV-sel"]; npmvsel->yacc; npmv [label="NPMV"]; npdivlog [label="NP/log"]; npdivlog->npdivpoly; npinterus [label="NP insersect US"]; npiconpdivpoly [label="(NP intersect coNP)/poly"]; npiconp->npiconpdivpoly; npiconp->np; npiconp->conp; npiconp [label="NP intersect coNP"]; npi [label="NPI"]; npi->np; npdashc [label="NP_C"]; pdashr->pdashc; pdashc->npdashc; npcc [label="NP^CC"]; npc [label="NPC"]; nlog [label="NLOG"]; nlin [label="NLIN"]; niszkh [label="NISZK_h"]; niszk [label="NISZK"]; niqszk [label="NIQSZK"]; niqszk->yacc; nexpdivpoly [label="NEXP/poly"]; nexpdivpoly->yacc; nexpinterconexp [label="NEXP intersect coNEXP"]; nexpinterconexp->nexp; neee [label="NEEE"]; nee->neee; nedivpoly [label="NE/poly"]; nc2 [label="NC^2"]; nc1 [label="NC^1"]; mtc0 [label="mTC^0"]; mpdivpoly [label="mP/poly"]; mpdivpoly->pdivpoly; mpc [label="MPC"]; mpc->yacc; mp2 [label="MP"]; modzkl [label="ModZ_k L"]; modp [label="ModP"]; modkp [label="Mod_k P"]; modkl [label="Mod_k L"]; mnp [label="mNP"]; mnl [label="mNL"]; mnc1 [label="mNC^1"]; ml [label="mL"]; mkp [label="(M_k)P"]; mkp->np; mipexp [label="MIP_EXP"]; mip->mipexp; mipstar21 [label="MIP*[2,1]"]; minpb [label="MinPB"]; minpb->np; mconl [label="mcoNL"]; maxsnp0 [label="MaxSNP^0"]; maxsnp0->maxsnp; maxsnp [label="MaxSNP"]; maxsnp->np; maxpb [label="MaxPB"]; maxnp [label="MaxNP"]; maexp [label="MA-EXP"]; mae->maexp; mae [label="MA-E"]; ma->mae; mac0 [label="MAC^0"]; maprime [label="MA'"]; maprime->ma; lwpp [label="LWPP"]; logsnp [label="LOGSNP"]; lognp [label="LogNP"]; logfewnl [label="LogFewNL"]; logfew [label="LogFew"]; logfew->modkl; lkp [label="L_k P"]; lkp->np; lin [label="LIN"]; lin->nlin; lin->p; nlin->np; ipp [label="IPP"]; npspace->ipp; iclogpoly [label="IC[log,poly]"]; hkp [label="H_k P"]; hkp->np; heurbtime [label="HeurBPTIME(f(n))"]; heurbtime->yacc; heurbpp [label="HeurBPP"]; heurbpp->yacc; gt [label="G[t]"]; gt->yacc; gpcd [label="GPCD(r(n),q(n))"]; gc [label="GC(s(n),C)"]; gc->yacc; gapp [label="GapP"]; gapp->yacc; gapl [label="GapL"]; gapl->yacc; gapac0 [label="GapAC^0"]; ganspace [label="GAN-SPACE(f(n))"]; ga [label="GA"]; ftime [label="F-TIME(f(n))"]; ftape [label="F-TAPE(f(n))"]; ftime->ftape; ftape->yacc; frip [label="frIP"]; fqma [label="FQMA"]; fqma->yacc; fptas [label="FPTAS"]; fptsu [label="FPT_su"]; fptnu [label="FPT_nu"]; fpt [label="FPT"]; fpras [label="FPRAS"]; fpras->sharpp; fpr [label="FPR"]; fpnplog [label="FP^NP[log]"]; fp->fnplog; fp [label="FP"]; foll [label="FOLL"]; fo [label="FO(t(n))"]; fo->yacc; fnp [label="FNP"]; fnldivpoly [label="FNL/poly"]; fnl [label="FNL"]; fnl->yacc; fh [label="FH"]; fh->yacc; fewp [label="FewP"]; few [label="Few"]; fbqp [label="FBQP"]; fbqp->yacc; expspace [label="EXPSPACE"]; existsniszk [label="\exists NISZK"]; existsbpp [label="\exists BPP"]; espace [label="ESPACE"]; eqtime [label="EQTIME(f(n))"]; eqp->eqtime; eqp [label="EQP"]; eqp->bqp; eqbp [label="k-EQBP"]; eptas [label="EPTAS"]; elpk [label="EL_k P"]; elpk->yacc; elementary [label="ELEMENTARY"]; eh [label="EH"]; neicone [label="NE intersect coNE"]; neicone->ne; neicone->cone; eespace [label="EESPACE"]; ee->eespace; dynthc0 [label="Dyn-Thc^0"]; dynthc0->yacc; dynfo [label="Dyn-FO"]; dynfo->yacc; dtisp [label="DTISP(t(n),s(n))"]; dtisp->yacc; dtime [label="DTIME(f(n))"]; dtime->dspace; dspace [label="DSPACE(f(n)),RevSPACE(f(n))"]; dspace2 [label="DSPACE(f(n)^2"]; dspace->dspace2; prspace->dspace2; np->pcp; mip->pcp; dqp [label="DQP"]; dp [label="DP"]; dp->yacc; distnp [label="DistNP"]; distnp->yacc; disnp [label="DisNP"]; disnp->yacc; diffac0 [label="DiffAC^0"]; diffac0->yacc; deltarp [label="\delta-RP"]; rp->deltarp; deltabpp [label="\delta-BPP"]; bpp->deltabpp; delta2p [label="\Delta_2 P"]; dsharpp [label="D#P"]; dsharpp->yacc; czk [label="CZK"]; csize [label="CSIZE(f(n))"]; csize->yacc; cp [label="CP"]; cpeqpp [label="CP_= PP"] ceqp->cpeqpp; cous [label="coUS"]; coucc [label="coUCC"]; coucc->yacc; conp [label="coNP"]; conexp [label="coNEXP"]; cone [label="coNE"]; compnp [label="compNP"]; compip [label="compIP"]; coh [label="Coh"]; coh->yacc; cnp [label="CNP"]; c [label="C_k P"]; c->ch; ch [label="CH"]; clog [label="CLOG"]; cfl [label="CFL"]; ceql [label="C_= L"]; ceqac0 [label="C_= AC^0"]; ceqac0->yacc; bqtime [label="BQTIME(f(n))"]; bqp->bqtime; bqpttdivpoly [label="BQP_tt /poly"]; bqpttdivpoly->bqpdivpoly; bqpdashobdd [label="BQP-OBDD"]; bqnc [label="BQNC"]; bptime [label="BPTIME(f(n))"]; bptime->bpspace; bpspace->yacc; bpspace [label="BPSPACE(f(n))"]; bpqp [label="BPQP"]; bpqp->bptime; bppdashobdd [label="BPP-OBDD"]; bppkt [label="BPP^KT"]; bppkt->yacc; bppcc [label="BPP^CC"]; bphspace [label="BP_H SPACE(f(n))"]; bpee [label="BPEE"]; bpe [label="BPE"]; bh [label="BH"]; betap [label="\beta P"]; awt [label="AW[t]"]; awstar [label="AW[*]"]; awsat [label="AW[SAT]"]; awpp [label="AWPP"]; awp [label="AW[P]"]; avp [label="AvP"]; avp->ave; ave [label="AvE"]; ave->yacc; avbpp [label="AVBPP"]; bpp->avbpp; aucspace [label="AUC-SPACE(f(n))"]; apx [label="APX"]; app2 [label="APP"]; ap2 [label="AP"]; amppbqp [label="AmpP-BQP"]; amppbqp->ph; ampmp [label="AmpMP"]; ampolylog [label="AM[polylog]"]; am->ampolylog; amdashexp [label="AM-EXP"]; algpdivpoly [label="AlgP/poly"]; algpdivpoly->yacc; ah [label="AH"]; ah->yacc; acc0 [label="ACC^0"]; ac0m [label="AC^0[m]"]; ac0 [label="AC^0"]; a0pp [label="A_0 PP"]; paritysac1 [label="+SAC^1"]; parityp [label="+P"]; parityl [label="+L"]; parityexp [label="+EXP"]; parityexp->nexp; sharpwt [label="#W[t]"]; sharpwt->yacc; sharpp [label="#P"]; sharpldivpoly [label="#L/poly"]; sharpl [label="#L"]; am [label="AM"]; gi [label="GI"]; qip [label="QIP,QMAM,QIP(3)"]; qma [label="QMA,QIP(1),QMA+"]; pl [label="PL,PL^PL"]; p [label="P,AL"]; np [label="NP,BH_1,PCP(0,poly(n)),PCP(log n, log n),PCP(log n,1),SO-E"]; mip [label="MIP,PCP(poly(n),poly(n))"]; ac [label="AC,NC"]; logcfl [label="LOGCFL,SAC^1"]; bqp [label="BQP,QMA_log,BQP^BQP"]; ppads [label="PPADS,PSK"]; pp [label="PP,PostBQP,PP^BPP,PP^BQP"]; ppa [label="PPA,PODN"]; ppdashph->psharpp; ppdashph [label="PP^PH"]; psharpp [label="P^#P,P^PP,P^MP,P^AmpMP,P^ModP"]; nldivpoly [label="NL/poly,UL/poly"]; neexp [label="NEEXP,MIP_EXP"]; nexp [label="NEXP,MIP,PCP(poly(n),poly(n)),QMIP_ne"]; mp [label="mP,mAL"]; pbp [label="PBP,L/poly"]; npspace [label="NPSPACE, PSPACE, PPSPACE,IP,AP,SAPTIME,AUC-SPACE(poly(n)),PQUERY,PCD(log n,1)"]; npspace->pcd; szk [label="SZK, HVSZK, SZK_h"]; nspace [label="NSPACE(n), CSL"]; nl [label="NL, coNL"]; l [label="L,SL,coSL"]; ceqp [label="C_= P, coNQP"]; coceqp [label="coC_= P,NQP"]; check [label="Check, frIP intersect cofrIP"]; ul [label="UL"]; rl [label="RL"]; amintercoam [label="AM intersect coAM"]; npdivpoly [label="NP/poly"]; ppp [label="PPP"]; bpp [label="BPP"]; bqpdivlog [label="BQP/log"]; bqpdivqlog [label="BQP/qlog"]; bpl [label="BPL"]; sc2 [label="SC^2"]; sc [label="SC"]; pdashobdd [label="P-OBDD"]; plinfinity [label="PL_infinity"]; parityldivpoly [label="+L/poly"]; corp [label="coRP"]; rp [label="RP"]; ma [label="MA"]; pdivpoly [label="P/poly"]; pdivlog [label="P/log"]; e [label="E"]; ee [label="EE"]; exp [label="EXP"]; ne [label="NE"]; eexp [label="EEXP"]; nee [label="NEE"]; bpppath [label="BPP_path"]; expdivpoly [label="EXP/poly"]; bqpdivqpoly [label="BQP/qpoly"]; bqpdivpoly [label="BQP/poly"]; ppdivpoly [label="PP/poly"]; coam [label="coAM"]; nc0 [label="NC^0"]; det [label="DET"]; sharpac0 [label="#AC^0"]; zero1npc [label="0-1-NP_C"] label="Complexity Zoo Taxonomy - created by Chad Brewbaker -last updated on Dec. 9, 2004 - based off of Scott Aaronson's http://www.complexityzoo.com - Please email any errors or additions to chad.brewbaker@gmail.com" }