All about Weak pigeonhole principle (\(n^2\) pigeons, n holes)

Proof Systems

• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Resolution is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Truth table is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Tree-like resolution is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Regular resolution is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Ordered resolution is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Pool resolution is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Linear resolution is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Reversible resolution is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Cutting Planes is polynomial
  • Source: CP → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Tree-like Cutting Planes is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Cutting Planes with Unary Coefficients is polynomial
  • Source: uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Semantic Cutting Planes is polynomial
  • Source: semanticCP → CP → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Cutting Planes with Saturation is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Stabbing Planes is polynomial
  • Source: SP → uSP → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Stabbing Planes with Unary Coefficients is polynomial
  • Source: uSP → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Res(CP) is polynomial
  • Source: Res(CP) → CP → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Res(LP) is polynomial
  • Source: Res(LP) → uRes(LP) → uRes(CP) → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Res(CP) with unary coefficients is polynomial
  • Source: uRes(CP) → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Res(LP) with unary coefficients is polynomial
  • Source: uRes(LP) → uRes(CP) → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Res(L\(\&\)P) is polynomial
  • Source: Res(L&P) → Res(LP) → uRes(LP) → uRes(CP) → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Res(L\(\&\)P) with unary coefficients is polynomial
  • Source: uRes(L&P) → uRes(LP) → uRes(CP) → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Polynomial Calculus over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Nullstellensatz over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
  • Source: ResLin_Z → uResLin_Z → uRes(CP) → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
  • Source: uResLin_Z → uRes(CP) → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in ResLin over \(\mathbb{F}_2\), Res(\(\oplus\)) is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\)) is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Polynomial Calculus over \(\mathbb{Q}\) is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Nullstellensatz over \(\mathbb{Q}\) is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Hitting is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Lift and Project is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Lift and Project with unary coefficients is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Positivstellensatz Calculus is polynomial
  • Source: PSC → PS → SoS → SA → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Positivstellensatz is polynomial
  • Source: PS → SoS → SA → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Lovász--Schrijver (LS) is polynomial
  • Source: LS → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Lovász--Schrijver with squares (LS\(_+\)) is polynomial
  • Source: LS+ → LS → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree is polynomial
  • Source: LSd+ → LS+ → LS → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree is polynomial
  • Source: LSn+ → sLSn+ → sLS+ → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Cone Proof System is polynomial
  • Source: CPS → IPS → extFrege → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in tl Lovász--Schrijver (LS) is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in static Lovász--Schrijver (static LS) is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in static Lovász--Schrijver, with squares of linear functions (static LS\(_+\)) is polynomial
  • Source: sLS+ → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\)) is polynomial
  • Source: sLSn+ → sLS+ → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Sum of Squares (Lasserre) is polynomial
  • Source: SoS → SA → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Sherali--Adams is polynomial
  • Source: SA → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Circular resolution is polynomial
  • Source: circRes → SA → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Unary Sherali--Adams is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Ideal Proof System is polynomial
  • Source: IPS → extFrege → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Extended Frege is polynomial
  • Source: extFrege → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Extended resolution is polynomial
  • Source: extRes → extFrege → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Frege is polynomial
  • Source: Frege → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in \(\mathrm{AC}^0\)-Frege is at most quasipolynomial
  • Source: AC0Frege → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in k-DNF Resolution is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in \(\mathrm{TC}^0\)-Frege is polynomial
  • Source: TC0Frege → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in \(\mathrm{AC}^0\)-Frege with mod 2 axioms is at most quasipolynomial
  • Source: AC0Frege+Mod2axioms → AC0Frege → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in \(\mathrm{AC}^0\)-Frege with mod 2 gates is at most quasipolynomial
  • Source: AC0(+)Frege → AC0Frege → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in OBDD(join,weakening) is polynomial
  • Source: OBDDjoinweak → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in LK is polynomial
  • Source: LK → Frege → PHP → PHP2nn → PHPn2n
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Zermelo-Fraenkl Set Theory with the Axiom of Choice is polynomial
  • Source: ZFC → extFrege → PHP → PHP2nn → PHPn2n

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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