All about Bitwise pigeonhole principle

Proof Systems

• The size complexity of Bitwise pigeonhole principle in Resolution is exponential
  • Source: bPHP → CP → uCP → Res
• The size complexity of Bitwise pigeonhole principle in Truth table is exponential
  • Source: bPHP → CP → tlCP → tlRes → ttp
• The size complexity of Bitwise pigeonhole principle in Tree-like resolution is exponential
  • Source: bPHP → CP → tlCP → tlRes
• The size complexity of Bitwise pigeonhole principle in Regular resolution is exponential
  • Source: bPHP → CP → uCP → Res → regRes
• The size complexity of Bitwise pigeonhole principle in Ordered resolution is exponential
  • Source: bPHP → CP → uCP → Res → regRes → ordRes
• The size complexity of Bitwise pigeonhole principle in Pool resolution is exponential
  • Source: bPHP → CP → uCP → Res → poolRes
• The size complexity of Bitwise pigeonhole principle in Linear resolution is exponential
  • Source: bPHP → CP → uCP → Res → linRes
• The size complexity of Bitwise pigeonhole principle in Reversible resolution is exponential
  • Source: bPHP → CP → uCP → Res → revRes
• The size complexity of Bitwise pigeonhole principle in Cutting Planes is exponential
  • Source: HP17 Random Formulas, Monotone Circuits, and Interpolation.
• The size complexity of Bitwise pigeonhole principle in Tree-like Cutting Planes is exponential
  • Source: bPHP → CP → tlCP
• The size complexity of Bitwise pigeonhole principle in Cutting Planes with Unary Coefficients is exponential
  • Source: bPHP → CP → uCP
• The size complexity of Bitwise pigeonhole principle in Semantic Cutting Planes is [missing?]
• The size complexity of Bitwise pigeonhole principle in Cutting Planes with Saturation is exponential
  • Source: bPHP → CP → uCP → Res → saturationCP
• The size complexity of Bitwise pigeonhole principle in Stabbing Planes is [missing?]
• The size complexity of Bitwise pigeonhole principle in Stabbing Planes with Unary Coefficients is exponential
  • Source: bPHP → CP → uSP
• The size complexity of Bitwise pigeonhole principle in Res(CP) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Res(LP) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Res(CP) with unary coefficients is [missing?]
• The size complexity of Bitwise pigeonhole principle in Res(LP) with unary coefficients is [missing?]
• The size complexity of Bitwise pigeonhole principle in Res(L\(\&\)P) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Res(L\(\&\)P) with unary coefficients is [missing?]
• The size complexity of Bitwise pigeonhole principle in Semantic degree-k threshold system, treelike version is exponential
  • Source: IR21 Proof Complexity of Natural Formulas via Communication Arguments.
• The size complexity of Bitwise pigeonhole principle in Polynomial Calculus over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Nullstellensatz over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Bitwise pigeonhole principle in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Bitwise pigeonhole principle in unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Bitwise pigeonhole principle in ResLin over \(\mathbb{F}_2\), Res(\(\oplus\)) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\)) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Polynomial Calculus over \(\mathbb{Q}\) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Nullstellensatz over \(\mathbb{Q}\) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Hitting is exponential
  • Source: bPHP → CP → tlCP → tlRes → hit
• The size complexity of Bitwise pigeonhole principle in Lift and Project is [missing?]
• The size complexity of Bitwise pigeonhole principle in Lift and Project with unary coefficients is exponential
  • Source: bPHP → CP → uCP → uL&P
• The size complexity of Bitwise pigeonhole principle in Positivstellensatz Calculus is [missing?]
• The size complexity of Bitwise pigeonhole principle in Positivstellensatz is [missing?]
• The size complexity of Bitwise pigeonhole principle in Lovász--Schrijver (LS) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree is [missing?]
• The size complexity of Bitwise pigeonhole principle in Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree is [missing?]
• The size complexity of Bitwise pigeonhole principle in Cone Proof System is [missing?]
• The size complexity of Bitwise pigeonhole principle in tl Lovász--Schrijver (LS) is exponential
  • Source: bPHP → tlTH(k) → tlLSd+ → tlLS+ → tlLS
• The size complexity of Bitwise pigeonhole principle in Lovász--Schrijver with squares (LS\(_+\)) is exponential
  • Source: bPHP → tlTH(k) → tlLSd+ → tlLS+
• The size complexity of Bitwise pigeonhole principle in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike is exponential
  • Source: bPHP → tlTH(k) → tlLSd+
• The size complexity of Bitwise pigeonhole principle in static Lovász--Schrijver (static LS) is [missing?]
• The size complexity of Bitwise pigeonhole principle in static Lovász--Schrijver, with squares of linear functions (static LS\(_+\)) is [missing?]
• The size complexity of Bitwise pigeonhole principle in static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\)) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Sum of Squares (Lasserre) is [missing?]
• The size complexity of Bitwise pigeonhole principle in Sherali--Adams is [missing?]
• The size complexity of Bitwise pigeonhole principle in Circular resolution is [missing?]
• The size complexity of Bitwise pigeonhole principle in Unary Sherali--Adams is [missing?]
• The size complexity of Bitwise pigeonhole principle in Ideal Proof System is [missing?]
• The size complexity of Bitwise pigeonhole principle in Extended Frege is [missing?]
• The size complexity of Bitwise pigeonhole principle in Extended resolution is [missing?]
• The size complexity of Bitwise pigeonhole principle in Frege is [missing?]
• The size complexity of Bitwise pigeonhole principle in \(\mathrm{AC}^0\)-Frege is [missing?]
• The size complexity of Bitwise pigeonhole principle in k-DNF Resolution is [missing?]
• The size complexity of Bitwise pigeonhole principle in \(\mathrm{TC}^0\)-Frege is [missing?]
• The size complexity of Bitwise pigeonhole principle in \(\mathrm{AC}^0\)-Frege with mod 2 axioms is [missing?]
• The size complexity of Bitwise pigeonhole principle in \(\mathrm{AC}^0\)-Frege with mod 2 gates is [missing?]
• The size complexity of Bitwise pigeonhole principle in OBDD(join,weakening) is [missing?]
• The size complexity of Bitwise pigeonhole principle in LK is [missing?]
• The size complexity of Bitwise pigeonhole principle in Zermelo-Fraenkl Set Theory with the Axiom of Choice is [missing?]

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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