All about Flow

Proof Systems

• The size complexity of Flow in Resolution is exponential
  • Source: flow → PC_F2 → Res
• The size complexity of Flow in Truth table is exponential
  • Source: flow → PC_F2 → NS_F2 → tlRes → ttp
• The size complexity of Flow in Tree-like resolution is exponential
  • Source: flow → PC_F2 → NS_F2 → tlRes
• The size complexity of Flow in Regular resolution is exponential
  • Source: flow → PC_F2 → Res → regRes
• The size complexity of Flow in Ordered resolution is exponential
  • Source: flow → PC_F2 → Res → regRes → ordRes
• The size complexity of Flow in Pool resolution is exponential
  • Source: flow → PC_F2 → Res → poolRes
• The size complexity of Flow in Linear resolution is exponential
  • Source: flow → PC_F2 → Res → linRes
• The size complexity of Flow in Reversible resolution is exponential
  • Source: flow → PC_F2 → Res → revRes
• The size complexity of Flow in Cutting Planes is [missing?]
• The size complexity of Flow in Tree-like Cutting Planes is [missing?]
• The size complexity of Flow in Cutting Planes with Unary Coefficients is [missing?]
• The size complexity of Flow in Semantic Cutting Planes is [missing?]
• The size complexity of Flow in Cutting Planes with Saturation is exponential
  • Source: flow → PC_F2 → Res → saturationCP
• The size complexity of Flow in Stabbing Planes is [missing?]
• The size complexity of Flow in Stabbing Planes with Unary Coefficients is [missing?]
• The size complexity of Flow in Res(CP) is [missing?]
• The size complexity of Flow in Res(LP) is [missing?]
• The size complexity of Flow in Res(CP) with unary coefficients is [missing?]
• The size complexity of Flow in Res(LP) with unary coefficients is [missing?]
• The size complexity of Flow in Res(L\(\&\)P) is [missing?]
• The size complexity of Flow in Res(L\(\&\)P) with unary coefficients is [missing?]
• The size complexity of Flow in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Flow in Polynomial Calculus over \(\mathbb{F}_2\) is exponential
  • Source: AR03 Lower Bounds for Polynomial Calculus: Non-Binomial Case.
• The size complexity of Flow in Nullstellensatz over \(\mathbb{F}_2\) is exponential
  • Source: flow → PC_F2 → NS_F2
• The size complexity of Flow in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Flow in unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Flow in ResLin over \(\mathbb{F}_2\), Res(\(\oplus\)) is [missing?]
• The size complexity of Flow in Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\)) is [missing?]
• The size complexity of Flow in Polynomial Calculus over \(\mathbb{Q}\) is exponential
  • Source: AR03 Lower Bounds for Polynomial Calculus: Non-Binomial Case.
• The size complexity of Flow in Nullstellensatz over \(\mathbb{Q}\) is exponential
  • Source: flow → PC_Q → NS_Q
• The size complexity of Flow in Hitting is exponential
  • Source: flow → PC_F2 → NS_F2 → tlRes → hit
• The size complexity of Flow in Lift and Project is [missing?]
• The size complexity of Flow in Lift and Project with unary coefficients is [missing?]
• The size complexity of Flow in Positivstellensatz Calculus is [missing?]
• The size complexity of Flow in Positivstellensatz is [missing?]
• The size complexity of Flow in Lovász--Schrijver (LS) is [missing?]
• The size complexity of Flow in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Flow in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree is [missing?]
• The size complexity of Flow in Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree is [missing?]
• The size complexity of Flow in Cone Proof System is [missing?]
• The size complexity of Flow in tl Lovász--Schrijver (LS) is [missing?]
• The size complexity of Flow in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Flow in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike is [missing?]
• The size complexity of Flow in static Lovász--Schrijver (static LS) is [missing?]
• The size complexity of Flow in static Lovász--Schrijver, with squares of linear functions (static LS\(_+\)) is [missing?]
• The size complexity of Flow in static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\)) is [missing?]
• The size complexity of Flow in Sum of Squares (Lasserre) is [missing?]
• The size complexity of Flow in Sherali--Adams is [missing?]
• The size complexity of Flow in Circular resolution is [missing?]
• The size complexity of Flow in Unary Sherali--Adams is [missing?]
• The size complexity of Flow in Ideal Proof System is [missing?]
• The size complexity of Flow in Extended Frege is [missing?]
• The size complexity of Flow in Extended resolution is [missing?]
• The size complexity of Flow in Frege is [missing?]
• The size complexity of Flow in \(\mathrm{AC}^0\)-Frege is [missing?]
• The size complexity of Flow in k-DNF Resolution is [missing?]
• The size complexity of Flow in \(\mathrm{TC}^0\)-Frege is [missing?]
• The size complexity of Flow in \(\mathrm{AC}^0\)-Frege with mod 2 axioms is [missing?]
• The size complexity of Flow in \(\mathrm{AC}^0\)-Frege with mod 2 gates is [missing?]
• The size complexity of Flow in OBDD(join,weakening) is [missing?]
• The size complexity of Flow in LK is [missing?]
• The size complexity of Flow 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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