All about Tseitin over \(\mathbb{F}_2\)

Proof Systems

• The size complexity of Tseitin over \(\mathbb{F}_2\) in Resolution is exponential
  • Source: Urquhart87 Hard examples for resolution.
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Truth table is exponential
  • Source: tseitin → Res → regRes → tlRes → ttp
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Tree-like resolution is exponential
  • Source: tseitin → Res → regRes → tlRes
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Regular resolution is exponential
  • Source: tseitin → Res → regRes
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Ordered resolution is exponential
  • Source: tseitin → Res → regRes → ordRes
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Pool resolution is exponential
  • Source: tseitin → Res → poolRes
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Linear resolution is exponential
  • Source: tseitin → Res → linRes
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Reversible resolution is exponential
  • Source: tseitin → Res → revRes
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Cutting Planes is at most quasipolynomial
  • Source: DT20 On the Complexity of Branching Proofs.
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Tree-like Cutting Planes is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Cutting Planes with Unary Coefficients is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Semantic Cutting Planes is at most quasipolynomial
  • Source: semanticCP → CP → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Cutting Planes with Saturation is exponential
  • Source: tseitin → Res → saturationCP
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Stabbing Planes is at most quasipolynomial
  • Source: BFIKPPR18 Stabbing Planes.
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Stabbing Planes with Unary Coefficients is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Res(CP) is polynomial
  • Source: Res(CP) → Res(LP) → uRes(LP) → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Res(LP) is polynomial
  • Source: Res(LP) → uRes(LP) → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Res(CP) with unary coefficients is polynomial
  • Source: uRes(CP) → uRes(LP) → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Res(LP) with unary coefficients is polynomial
  • Source: HirschK06 Several notes on the power of Gomory-Chvátal cuts.
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Res(L\(\&\)P) is polynomial
  • Source: Res(L&P) → Res(LP) → uRes(LP) → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Res(L\(\&\)P) with unary coefficients is polynomial
  • Source: uRes(L&P) → uRes(LP) → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Polynomial Calculus over \(\mathbb{F}_2\) is polynomial
  • Source: PC_F2 → NS_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Nullstellensatz over \(\mathbb{F}_2\) is polynomial
  • Source: [citation needed]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
  • Source: ResLin_Z → uResLin_Z → ResLin_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
  • Source: uResLin_Z → ResLin_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in ResLin over \(\mathbb{F}_2\), Res(\(\oplus\)) is polynomial
  • Source: [citation needed]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\)) is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Polynomial Calculus over \(\mathbb{Q}\) is exponential
  • Source: BGIP01 Linear Gaps between Degrees for the Polynomial Calculus Modulo Distinct Primes.
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Nullstellensatz over \(\mathbb{Q}\) is exponential
  • Source: tseitin → PC_Q → NS_Q
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Hitting is exponential
  • Source: tseitin → Res → regRes → tlRes → hit
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Lift and Project is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Lift and Project with unary coefficients is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Positivstellensatz Calculus is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Positivstellensatz is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Lovász--Schrijver (LS) is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree is polynomial
  • Source: GHP02 Complexity of semialgebraic proofs
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree is polynomial
  • Source: LSn+ → LSd+ → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Cone Proof System is polynomial
  • Source: CPS → LSn+ → LSd+ → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in tl Lovász--Schrijver (LS) is exponential
  • Source: tseitin → sLS+ → tlLS+ → tlLS
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Lovász--Schrijver with squares (LS\(_+\)) is exponential
  • Source: tseitin → sLS+ → tlLS+
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike is [missing?]
• The size complexity of Tseitin over \(\mathbb{F}_2\) in static Lovász--Schrijver (static LS) is exponential
  • Source: tseitin → sLS+ → sLS
• The size complexity of Tseitin over \(\mathbb{F}_2\) in static Lovász--Schrijver, with squares of linear functions (static LS\(_+\)) is exponential
  • Source: IK07 Lower bounds of static Lovász-Schrijver calculus proofs for Tseitin tautologies
• The size complexity of Tseitin over \(\mathbb{F}_2\) in static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\)) is exponential
  • Source: tseitin → SoS → sLSn+
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Sum of Squares (Lasserre) is exponential
  • Source: AtseriasH19 Size-Degree Trade-Offs for Sums-of-Squares and Positivstellensatz Proofs.
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Sherali--Adams is exponential
  • Source: tseitin → SoS → SA
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Circular resolution is exponential
  • Source: tseitin → SoS → SA → circRes
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Unary Sherali--Adams is exponential
  • Source: tseitin → SoS → SA → uSA
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Ideal Proof System is polynomial
  • Source: IPS → extFrege → Frege → AC0(+)Frege → ResLin_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Extended Frege is polynomial
  • Source: extFrege → Frege → AC0(+)Frege → ResLin_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Extended resolution is polynomial
  • Source: extRes → extFrege → Frege → AC0(+)Frege → ResLin_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Frege is polynomial
  • Source: Frege → AC0(+)Frege → ResLin_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in \(\mathrm{AC}^0\)-Frege is exponential
  • Source: BenSasson02 Hard examples for the bounded depth Frege proof system.
• The size complexity of Tseitin over \(\mathbb{F}_2\) in k-DNF Resolution is exponential
  • Source: tseitin → AC0Frege → Res-k
• The size complexity of Tseitin over \(\mathbb{F}_2\) in \(\mathrm{TC}^0\)-Frege is polynomial
  • Source: TC0Frege → Res(CP) → Res(LP) → uRes(LP) → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in \(\mathrm{AC}^0\)-Frege with mod 2 axioms is polynomial
  • Source: AC0Frege+Mod2axioms → NS_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in \(\mathrm{AC}^0\)-Frege with mod 2 gates is polynomial
  • Source: AC0(+)Frege → ResLin_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in OBDD(join,weakening) is polynomial
  • Source: AKV04 Constraint Propagation as a Proof System.
• The size complexity of Tseitin over \(\mathbb{F}_2\) in LK is polynomial
  • Source: LK → Frege → AC0(+)Frege → ResLin_F2 → tseitin
• The size complexity of Tseitin over \(\mathbb{F}_2\) in Zermelo-Fraenkl Set Theory with the Axiom of Choice is polynomial
  • Source: ZFC → Res(CP) → Res(LP) → uRes(LP) → tseitin

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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