All about Tseitin \(\mathbb{F}_2\) \(\circ\) IND

Proof Systems

• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Resolution is exponential
  • Source: ts+ind → CP → uCP → Res
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Truth table is exponential
  • Source: ts+ind → CP → tlCP → tlRes → ttp
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Tree-like resolution is exponential
  • Source: ts+ind → CP → tlCP → tlRes
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Regular resolution is exponential
  • Source: ts+ind → CP → uCP → Res → regRes
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Ordered resolution is exponential
  • Source: ts+ind → CP → uCP → Res → regRes → ordRes
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Pool resolution is exponential
  • Source: ts+ind → CP → uCP → Res → poolRes
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Linear resolution is exponential
  • Source: ts+ind → CP → uCP → Res → linRes
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Reversible resolution is exponential
  • Source: ts+ind → CP → uCP → Res → revRes
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Cutting Planes is exponential
  • Source: GGKS20 Monotone Circuit Lower Bounds from Resolution.
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Tree-like Cutting Planes is exponential
  • Source: ts+ind → CP → tlCP
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Cutting Planes with Unary Coefficients is exponential
  • Source: ts+ind → CP → uCP
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Semantic Cutting Planes is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Cutting Planes with Saturation is exponential
  • Source: ts+ind → CP → uCP → Res → saturationCP
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Stabbing Planes is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Stabbing Planes with Unary Coefficients is exponential
  • Source: ts+ind → CP → uSP
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Res(CP) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Res(LP) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Res(CP) with unary coefficients is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Res(LP) with unary coefficients is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Res(L\(\&\)P) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Res(L\(\&\)P) with unary coefficients is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Polynomial Calculus over \(\mathbb{F}_2\) is at most quasipolynomial
  • Source: PC_F2 → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Nullstellensatz over \(\mathbb{F}_2\) is at most quasipolynomial
  • Source: GKRS19 Adventures in Monotone Complexity and TFNP.
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in ResLin over \(\mathbb{F}_2\), Res(\(\oplus\)) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\)) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Polynomial Calculus over \(\mathbb{Q}\) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Nullstellensatz over \(\mathbb{Q}\) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Hitting is exponential
  • Source: ts+ind → CP → tlCP → tlRes → hit
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Lift and Project is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Lift and Project with unary coefficients is exponential
  • Source: ts+ind → CP → uCP → uL&P
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Positivstellensatz Calculus is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Positivstellensatz is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Lovász--Schrijver (LS) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Cone Proof System is at most quasipolynomial
  • Source: CPS → IPS → extFrege → Frege → AC0(+)Frege → AC0Frege+Mod2axioms → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in tl Lovász--Schrijver (LS) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in static Lovász--Schrijver (static LS) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in static Lovász--Schrijver, with squares of linear functions (static LS\(_+\)) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\)) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Sum of Squares (Lasserre) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Sherali--Adams is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Circular resolution is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Unary Sherali--Adams is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Ideal Proof System is at most quasipolynomial
  • Source: IPS → extFrege → Frege → AC0(+)Frege → AC0Frege+Mod2axioms → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Extended Frege is at most quasipolynomial
  • Source: extFrege → Frege → AC0(+)Frege → AC0Frege+Mod2axioms → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Extended resolution is at most quasipolynomial
  • Source: extRes → extFrege → Frege → AC0(+)Frege → AC0Frege+Mod2axioms → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Frege is at most quasipolynomial
  • Source: Frege → AC0(+)Frege → AC0Frege+Mod2axioms → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in \(\mathrm{AC}^0\)-Frege is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in k-DNF Resolution is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in \(\mathrm{TC}^0\)-Frege is at most quasipolynomial
  • Source: TC0Frege → AC0(+)Frege → AC0Frege+Mod2axioms → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in \(\mathrm{AC}^0\)-Frege with mod 2 axioms is at most quasipolynomial
  • Source: AC0Frege+Mod2axioms → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in \(\mathrm{AC}^0\)-Frege with mod 2 gates is at most quasipolynomial
  • Source: AC0(+)Frege → AC0Frege+Mod2axioms → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in OBDD(join,weakening) is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in LK is at most quasipolynomial
  • Source: LK → Frege → AC0(+)Frege → AC0Frege+Mod2axioms → NS_F2 → ts+ind
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Zermelo-Fraenkl Set Theory with the Axiom of Choice is at most quasipolynomial
  • Source: ZFC → extFrege → Frege → AC0(+)Frege → AC0Frege+Mod2axioms → NS_F2 → ts+ind

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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