All about String of pearls

Proof Systems

• The size complexity of String of pearls in Resolution is polynomial
  • Source: Res → regRes → pearl
• The size complexity of String of pearls in Truth table is [missing?]
• The size complexity of String of pearls in Tree-like resolution is at most quasipolynomial
  • Source: Johannsen01 Exponential Incomparability of Tree-like and Ordered Resolution
• The size complexity of String of pearls in Regular resolution is polynomial
  • Source: BEGJ00 On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems.
• The size complexity of String of pearls in Ordered resolution is exponential
  • Source: BEGJ00 On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems.
• The size complexity of String of pearls in Pool resolution is polynomial
  • Source: poolRes → regRes → pearl
• The size complexity of String of pearls in Linear resolution is at most quasipolynomial
  • Source: linRes → tlRes → pearl
• The size complexity of String of pearls in Reversible resolution is at most quasipolynomial
  • Source: revRes → tlRes → pearl
• The size complexity of String of pearls in Cutting Planes is polynomial
  • Source: CP → uCP → Res → regRes → pearl
• The size complexity of String of pearls in Tree-like Cutting Planes is at most quasipolynomial
  • Source: tlCP → tlRes → pearl
• The size complexity of String of pearls in Cutting Planes with Unary Coefficients is polynomial
  • Source: uCP → Res → regRes → pearl
• The size complexity of String of pearls in Semantic Cutting Planes is polynomial
  • Source: semanticCP → saturationCP → Res → regRes → pearl
• The size complexity of String of pearls in Cutting Planes with Saturation is polynomial
  • Source: saturationCP → Res → regRes → pearl
• The size complexity of String of pearls in Stabbing Planes is polynomial
  • Source: SP → uSP → uCP → Res → regRes → pearl
• The size complexity of String of pearls in Stabbing Planes with Unary Coefficients is polynomial
  • Source: uSP → uCP → Res → regRes → pearl
• The size complexity of String of pearls in Res(CP) is polynomial
  • Source: Res(CP) → CP → uCP → Res → regRes → pearl
• The size complexity of String of pearls in Res(LP) is polynomial
  • Source: Res(LP) → uRes(LP) → Res → regRes → pearl
• The size complexity of String of pearls in Res(CP) with unary coefficients is polynomial
  • Source: uRes(CP) → uCP → Res → regRes → pearl
• The size complexity of String of pearls in Res(LP) with unary coefficients is polynomial
  • Source: uRes(LP) → Res → regRes → pearl
• The size complexity of String of pearls in Res(L\(\&\)P) is polynomial
  • Source: Res(L&P) → Res(LP) → uRes(LP) → Res → regRes → pearl
• The size complexity of String of pearls in Res(L\(\&\)P) with unary coefficients is polynomial
  • Source: uRes(L&P) → uRes(LP) → Res → regRes → pearl
• The size complexity of String of pearls in Semantic degree-k threshold system, treelike version is at most quasipolynomial
  • Source: tlTH(k) → tlCP → tlRes → pearl
• The size complexity of String of pearls in Polynomial Calculus over \(\mathbb{F}_2\) is polynomial
  • Source: PC_F2 → Res → regRes → pearl
• The size complexity of String of pearls in Nullstellensatz over \(\mathbb{F}_2\) is at most quasipolynomial
  • Source: NS_F2 → tlRes → pearl
• The size complexity of String of pearls in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
  • Source: ResLin_Z → uResLin_Z → ResLin_F2 → Res → regRes → pearl
• The size complexity of String of pearls in unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
  • Source: uResLin_Z → ResLin_F2 → Res → regRes → pearl
• The size complexity of String of pearls in ResLin over \(\mathbb{F}_2\), Res(\(\oplus\)) is polynomial
  • Source: ResLin_F2 → Res → regRes → pearl
• The size complexity of String of pearls in Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\)) is at most quasipolynomial
  • Source: tlResLin_F2 → tlRes → pearl
• The size complexity of String of pearls in Polynomial Calculus over \(\mathbb{Q}\) is polynomial
  • Source: PC_Q → Res → regRes → pearl
• The size complexity of String of pearls in Nullstellensatz over \(\mathbb{Q}\) is at most quasipolynomial
  • Source: NS_Q → tlRes → pearl
• The size complexity of String of pearls in Hitting is at most quasipolynomial
  • Source: hit → tlRes → pearl
• The size complexity of String of pearls in Lift and Project is polynomial
  • Source: L&P → uL&P → Res → regRes → pearl
• The size complexity of String of pearls in Lift and Project with unary coefficients is polynomial
  • Source: uL&P → Res → regRes → pearl
• The size complexity of String of pearls in Positivstellensatz Calculus is polynomial
  • Source: PSC → PS → SoS → PC_Q → Res → regRes → pearl
• The size complexity of String of pearls in Positivstellensatz is polynomial
  • Source: PS → SoS → PC_Q → Res → regRes → pearl
• The size complexity of String of pearls in Lovász--Schrijver (LS) is polynomial
  • Source: LS → L&P → uL&P → Res → regRes → pearl
• The size complexity of String of pearls in Lovász--Schrijver with squares (LS\(_+\)) is polynomial
  • Source: LS+ → LS → L&P → uL&P → Res → regRes → pearl
• The size complexity of String of pearls in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree is polynomial
  • Source: LSd+ → LS+ → LS → L&P → uL&P → Res → regRes → pearl
• The size complexity of String of pearls in Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree is polynomial
  • Source: LSn+ → PSC → PS → SoS → PC_Q → Res → regRes → pearl
• The size complexity of String of pearls in Cone Proof System is polynomial
  • Source: CPS → IPS → extFrege → extRes → Res → regRes → pearl
• The size complexity of String of pearls in tl Lovász--Schrijver (LS) is at most quasipolynomial
  • Source: tlLS → tlRes → pearl
• The size complexity of String of pearls in Lovász--Schrijver with squares (LS\(_+\)) is at most quasipolynomial
  • Source: tlLS+ → tlLS → tlRes → pearl
• The size complexity of String of pearls in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike is at most quasipolynomial
  • Source: tlLSd+ → tlLS+ → tlLS → tlRes → pearl
• The size complexity of String of pearls in static Lovász--Schrijver (static LS) is at most quasipolynomial
  • Source: sLS → tlLS → tlRes → pearl
• The size complexity of String of pearls in static Lovász--Schrijver, with squares of linear functions (static LS\(_+\)) is at most quasipolynomial
  • Source: sLS+ → tlLS+ → tlLS → tlRes → pearl
• The size complexity of String of pearls in static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\)) is at most quasipolynomial
  • Source: sLSn+ → sLS+ → tlLS+ → tlLS → tlRes → pearl
• The size complexity of String of pearls in Sum of Squares (Lasserre) is polynomial
  • Source: SoS → PC_Q → Res → regRes → pearl
• The size complexity of String of pearls in Sherali--Adams is polynomial
  • Source: SA → circRes → Res → regRes → pearl
• The size complexity of String of pearls in Circular resolution is polynomial
  • Source: circRes → Res → regRes → pearl
• The size complexity of String of pearls in Unary Sherali--Adams is at most quasipolynomial
  • Source: uSA → revRes → tlRes → pearl
• The size complexity of String of pearls in Ideal Proof System is polynomial
  • Source: IPS → extFrege → extRes → Res → regRes → pearl
• The size complexity of String of pearls in Extended Frege is polynomial
  • Source: extFrege → extRes → Res → regRes → pearl
• The size complexity of String of pearls in Extended resolution is polynomial
  • Source: extRes → Res → regRes → pearl
• The size complexity of String of pearls in Frege is polynomial
  • Source: Frege → AC0Frege → Res-k → Res → regRes → pearl
• The size complexity of String of pearls in \(\mathrm{AC}^0\)-Frege is polynomial
  • Source: AC0Frege → Res-k → Res → regRes → pearl
• The size complexity of String of pearls in k-DNF Resolution is polynomial
  • Source: Res-k → Res → regRes → pearl
• The size complexity of String of pearls in \(\mathrm{TC}^0\)-Frege is polynomial
  • Source: TC0Frege → AC0Frege → Res-k → Res → regRes → pearl
• The size complexity of String of pearls in \(\mathrm{AC}^0\)-Frege with mod 2 axioms is polynomial
  • Source: AC0Frege+Mod2axioms → AC0Frege → Res-k → Res → regRes → pearl
• The size complexity of String of pearls in \(\mathrm{AC}^0\)-Frege with mod 2 gates is polynomial
  • Source: AC0(+)Frege → ResLin_F2 → Res → regRes → pearl
• The size complexity of String of pearls in OBDD(join,weakening) is polynomial
  • Source: OBDDjoinweak → uCP → Res → regRes → pearl
• The size complexity of String of pearls in LK is polynomial
  • Source: LK → Frege → AC0Frege → Res-k → Res → regRes → pearl
• The size complexity of String of pearls in Zermelo-Fraenkl Set Theory with the Axiom of Choice is polynomial
  • Source: ZFC → extFrege → extRes → Res → regRes → pearl

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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