All about Random CNF

Proof Systems

• The size complexity of Random CNF in Resolution is exponential
  • Source: CS88 Many Hard Examples for Resolution.
• The size complexity of Random CNF in Truth table is exponential
  • Source: random → Res → regRes → tlRes → ttp
• The size complexity of Random CNF in Tree-like resolution is exponential
  • Source: random → Res → regRes → tlRes
• The size complexity of Random CNF in Regular resolution is exponential
  • Source: random → Res → regRes
• The size complexity of Random CNF in Ordered resolution is exponential
  • Source: random → Res → regRes → ordRes
• The size complexity of Random CNF in Pool resolution is exponential
  • Source: random → Res → poolRes
• The size complexity of Random CNF in Linear resolution is exponential
  • Source: random → Res → linRes
• The size complexity of Random CNF in Reversible resolution is exponential
  • Source: random → Res → revRes
• The size complexity of Random CNF in Cutting Planes is [missing?]
• The size complexity of Random CNF in Tree-like Cutting Planes is [missing?]
• The size complexity of Random CNF in Cutting Planes with Unary Coefficients is [missing?]
• The size complexity of Random CNF in Semantic Cutting Planes is [missing?]
• The size complexity of Random CNF in Cutting Planes with Saturation is exponential
  • Source: random → Res → saturationCP
• The size complexity of Random CNF in Stabbing Planes is [missing?]
• The size complexity of Random CNF in Stabbing Planes with Unary Coefficients is [missing?]
• The size complexity of Random CNF in Res(CP) is [missing?]
• The size complexity of Random CNF in Res(LP) is [missing?]
• The size complexity of Random CNF in Res(CP) with unary coefficients is [missing?]
• The size complexity of Random CNF in Res(LP) with unary coefficients is [missing?]
• The size complexity of Random CNF in Res(L\(\&\)P) is [missing?]
• The size complexity of Random CNF in Res(L\(\&\)P) with unary coefficients is [missing?]
• The size complexity of Random CNF in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Random CNF in Polynomial Calculus over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Random CNF in Nullstellensatz over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Random CNF in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Random CNF in unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Random CNF in ResLin over \(\mathbb{F}_2\), Res(\(\oplus\)) is [missing?]
• The size complexity of Random CNF in Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\)) is [missing?]
• The size complexity of Random CNF in Polynomial Calculus over \(\mathbb{Q}\) is [missing?]
• The size complexity of Random CNF in Nullstellensatz over \(\mathbb{Q}\) is [missing?]
• The size complexity of Random CNF in Hitting is exponential
  • Source: random → Res → regRes → tlRes → hit
• The size complexity of Random CNF in Lift and Project is [missing?]
• The size complexity of Random CNF in Lift and Project with unary coefficients is [missing?]
• The size complexity of Random CNF in Positivstellensatz Calculus is [missing?]
• The size complexity of Random CNF in Positivstellensatz is [missing?]
• The size complexity of Random CNF in Lovász--Schrijver (LS) is [missing?]
• The size complexity of Random CNF in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Random CNF in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree is [missing?]
• The size complexity of Random CNF in Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree is [missing?]
• The size complexity of Random CNF in Cone Proof System is [missing?]
• The size complexity of Random CNF in tl Lovász--Schrijver (LS) is [missing?]
• The size complexity of Random CNF in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Random CNF in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike is [missing?]
• The size complexity of Random CNF in static Lovász--Schrijver (static LS) is [missing?]
• The size complexity of Random CNF in static Lovász--Schrijver, with squares of linear functions (static LS\(_+\)) is [missing?]
• The size complexity of Random CNF in static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\)) is [missing?]
• The size complexity of Random CNF in Sum of Squares (Lasserre) is [missing?]
• The size complexity of Random CNF in Sherali--Adams is [missing?]
• The size complexity of Random CNF in Circular resolution is [missing?]
• The size complexity of Random CNF in Unary Sherali--Adams is [missing?]
• The size complexity of Random CNF in Ideal Proof System is [missing?]
• The size complexity of Random CNF in Extended Frege is [missing?]
• The size complexity of Random CNF in Extended resolution is [missing?]
• The size complexity of Random CNF in Frege is [missing?]
• The size complexity of Random CNF in \(\mathrm{AC}^0\)-Frege is [missing?]
• The size complexity of Random CNF in k-DNF Resolution is [missing?]
• The size complexity of Random CNF in \(\mathrm{TC}^0\)-Frege is [missing?]
• The size complexity of Random CNF in \(\mathrm{AC}^0\)-Frege with mod 2 axioms is [missing?]
• The size complexity of Random CNF in \(\mathrm{AC}^0\)-Frege with mod 2 gates is [missing?]
• The size complexity of Random CNF in OBDD(join,weakening) is [missing?]
• The size complexity of Random CNF in LK is [missing?]
• The size complexity of Random CNF 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.

Licensed under CC BY 4.0