All about Weak Clique-Colouring (2m clique, m colours)

Proof Systems

• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Resolution is exponential
  • Source: CliqueColouring2mm → CP → uCP → Res
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Truth table is exponential
  • Source: CliqueColouring2mm → CP → tlCP → tlRes → ttp
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Tree-like resolution is exponential
  • Source: CliqueColouring2mm → CP → tlCP → tlRes
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Regular resolution is exponential
  • Source: CliqueColouring2mm → CP → uCP → Res → regRes
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Ordered resolution is exponential
  • Source: CliqueColouring2mm → CP → uCP → Res → regRes → ordRes
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Pool resolution is exponential
  • Source: CliqueColouring2mm → CP → uCP → Res → poolRes
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Linear resolution is exponential
  • Source: CliqueColouring2mm → CP → uCP → Res → linRes
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Reversible resolution is exponential
  • Source: CliqueColouring2mm → CP → uCP → Res → revRes
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Cutting Planes is exponential
  • Source: Pudlak97 Lower Bounds for Resolution and Cutting Plane Proofs and Monotone Computations.
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Tree-like Cutting Planes is exponential
  • Source: CliqueColouring2mm → CP → tlCP
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Cutting Planes with Unary Coefficients is exponential
  • Source: CliqueColouring2mm → CP → uCP
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Semantic Cutting Planes is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Cutting Planes with Saturation is exponential
  • Source: CliqueColouring2mm → CP → uCP → Res → saturationCP
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Stabbing Planes is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Stabbing Planes with Unary Coefficients is exponential
  • Source: CliqueColouring2mm → CP → uSP
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Res(CP) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Res(LP) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Res(CP) with unary coefficients is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Res(LP) with unary coefficients is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Res(L\(\&\)P) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Res(L\(\&\)P) with unary coefficients is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Polynomial Calculus over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Nullstellensatz over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in ResLin over \(\mathbb{F}_2\), Res(\(\oplus\)) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\)) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Polynomial Calculus over \(\mathbb{Q}\) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Nullstellensatz over \(\mathbb{Q}\) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Hitting is exponential
  • Source: CliqueColouring2mm → CP → tlCP → tlRes → hit
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Lift and Project is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Lift and Project with unary coefficients is exponential
  • Source: CliqueColouring2mm → CP → uCP → uL&P
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Positivstellensatz Calculus is polynomial
  • Source: PSC → PS → SoS → sLSn+ → CliqueColouring → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Positivstellensatz is polynomial
  • Source: PS → SoS → sLSn+ → CliqueColouring → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Lovász--Schrijver (LS) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree is polynomial
  • Source: LSd+ → CliqueColouring → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree is polynomial
  • Source: LSn+ → LSd+ → CliqueColouring → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Cone Proof System is polynomial
  • Source: CPS → LSn+ → LSd+ → CliqueColouring → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in tl Lovász--Schrijver (LS) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in static Lovász--Schrijver (static LS) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in static Lovász--Schrijver, with squares of linear functions (static LS\(_+\)) is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\)) is polynomial
  • Source: sLSn+ → CliqueColouring → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Sum of Squares (Lasserre) is polynomial
  • Source: SoS → sLSn+ → CliqueColouring → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Sherali--Adams is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Circular resolution is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Unary Sherali--Adams is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Ideal Proof System is at most quasipolynomial
  • Source: IPS → extFrege → Frege → AC0Frege → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Extended Frege is at most quasipolynomial
  • Source: extFrege → Frege → AC0Frege → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Extended resolution is at most quasipolynomial
  • Source: extRes → extFrege → Frege → AC0Frege → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Frege is at most quasipolynomial
  • Source: Frege → AC0Frege → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in \(\mathrm{AC}^0\)-Frege is at most quasipolynomial
  • Source: [citation needed]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in k-DNF Resolution is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in \(\mathrm{TC}^0\)-Frege is at most quasipolynomial
  • Source: TC0Frege → AC0Frege → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in \(\mathrm{AC}^0\)-Frege with mod 2 axioms is at most quasipolynomial
  • Source: AC0Frege+Mod2axioms → AC0Frege → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in \(\mathrm{AC}^0\)-Frege with mod 2 gates is at most quasipolynomial
  • Source: AC0(+)Frege → AC0Frege → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in OBDD(join,weakening) is polynomial
  • Source: OBDDjoinweak → CliqueColouring → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in LK is at most quasipolynomial
  • Source: LK → Frege → AC0Frege → CliqueColouring2mm
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Zermelo-Fraenkl Set Theory with the Axiom of Choice is at most quasipolynomial
  • Source: ZFC → extFrege → Frege → AC0Frege → CliqueColouring2mm

This database is still incomplete; missing data may indicate either the information was not yet recorded or an open problem. Users are encouraged to contribute missing proof systems and/or relations at https://gitlab.com/proofcomplexityzoo/zoo.

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