Complexity Zoology: Active Inclusion Diagram

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Arrows: ∀X: AX ⊆ BX and co.AX ⊆ BX      ∀X: AX ⊆ BX      ∀X: co.AX ⊆ BX      ∀X: cocap.AX ⊆ BX
Node colors: ∀X: AX ? BX          proven          disproven          open          unknown to us
If a cell has more than one color: left - regular inclusion; right - twisted inclusion; middle - weak inclusion.
Click on a node to select it as the "A" class. Press backslash (\) to switch between subset and superset status.
Shift-click to open to the "Class Relations" entry in a separate page.
See also: Complexity Zoology Introduction, Static Inclusion Diagram, Complexity Class Relations


diagram (NP-cap-coNP)/poly NP/poly PP/poly NE/poly (k>=5)-PBP NC^1 PBP L QNC^1 CSL +EXP EXPSPACE EESPACE EEXP +L +L/poly +SAC^1 AL P/poly NC^2 P BQP/poly +P ModP SF_2 AmpMP SF_3 +SAC^0 AC^0[2] QNC_f^0 ACC^0 QACC^0 NC 1NAuxPDA^p SAC^1 AC^1 2-PBP 3-PBP 4-PBP TC^0 TC^0/poly AC^0 AC^0/poly FOLL MAC^0 QAC^0 L/poly AH ALL AvgP HalfP NT P-Close P-Sel P/log UP beta_2P compNP AM AM[polylog] BPP^{NP} QAM Sigma_2P ZPP^{NP} IP Delta_3P SQG BP.PP QIP[2] RP^{NP} PSPACE MIP MIP* QIP AM_{EXP} IP_{EXP} NEXP^{NP} MIP_{EXP} EXPH APP PP P^{#P[1]} AVBPP HeurBPP EXP AWPP A_0PP Almost-PSPACE BPEXP BPEE MA_{EXP} MP AmpP-BQP BQP Sigma_3P BQP/log DQP NIQSZK QCMA YQP PH AvgE EE NEE E Nearly-P UE ZPE BH P^{NP[log]} BPP_{path} P^{NP[log^2]} BH_2 CH EXP/poly BPE MA_E EH EEE PEXP BPL PL SC NL/poly L^{DET} polyL BPP BPP/log BPQP Check FH N.BPP NISZK PZK TreeBQP WAPP XOR-MIP*[2,1] BPP/mlog QPSPACE frIP MA N.NISZK NISZK_h SZK SBP QMIP_{le} BPP//log BPP/rlog BQP/mlog BQP/qlog QRG ESPACE QSZK QMA BQP/qpoly BQP/mpoly CFL GCSL NLIN QCFL Q NLINSPACE RG CZK C_=L C_=P Coh DCFL LIN NEXP Delta_2P P^{QMA} S_2P P^{PP} QS_2P RG[1] NE RPE NEEXP NEEE ELEMENTARY PR R EP Mod_3P Mod_5P NP NP/one RP^{PromiseUP} US EQP LWPP ZQP WPP RQP NEXP/poly EXP^{NP} SEH Few P^{FewP} SPP FewL LFew NL SPL FewP FewUL LogFew RP ZPP RBQP YP ZBQP IC[log,poly] QMIP_{ne} QMIP R_HL UL RL MAJORITY PT_1 PL_{infty} MP^{#P} SF_4 RNC QNC QP NC^0 PL_1 QNC^0 SAC^0 NONE PARITY TALLY REG SPARSE NP/log NT* UAP QPLIN betaP compIP RE QMA(2) SUBEXP YPP

Last modified: Thu, 17 Aug 2006
Greg Kuperberg