All about Semantic degree-k threshold system, treelike version

Definition from: Lower Bounds for Lov[a-acute]sz--Schrijver Systems and Beyond Follow from Multiparty Communication Complexity.

Proof Systems

• Semantic degree-k threshold system, treelike version [missing?] Resolution
• Semantic degree-k threshold system, treelike version simulates Truth table
• Source: tlTH(k) → tlCP → tlRes → ttp
• Semantic degree-k threshold system, treelike version simulates Tree-like resolution
• Source: tlTH(k) → tlCP → tlRes
• Semantic degree-k threshold system, treelike version [missing?] Regular resolution
• Semantic degree-k threshold system, treelike version not simulated by Ordered resolution
• Source: tlTH(k) → tlCP → tlRes → pearl → ordRes
• Semantic degree-k threshold system, treelike version [missing?] Pool resolution
• Semantic degree-k threshold system, treelike version [missing?] Linear resolution
• Semantic degree-k threshold system, treelike version [missing?] Reversible resolution
• Semantic degree-k threshold system, treelike version [missing?] Cutting Planes
• Semantic degree-k threshold system, treelike version simulates Tree-like Cutting Planes
• Source: [subsystem]
• Semantic degree-k threshold system, treelike version [missing?] Cutting Planes with Unary Coefficients
• Semantic degree-k threshold system, treelike version [missing?] Semantic Cutting Planes
• Semantic degree-k threshold system, treelike version [missing?] Cutting Planes with Saturation
• Semantic degree-k threshold system, treelike version [missing?] Stabbing Planes
• Semantic degree-k threshold system, treelike version [missing?] Stabbing Planes with Unary Coefficients
• Semantic degree-k threshold system, treelike version [missing?] Res(CP)
• Semantic degree-k threshold system, treelike version [missing?] Res(LP)
• Semantic degree-k threshold system, treelike version [missing?] Res(CP) with unary coefficients
• Semantic degree-k threshold system, treelike version [missing?] Res(LP) with unary coefficients
• Semantic degree-k threshold system, treelike version [missing?] Res(L\(\&\)P)
• Semantic degree-k threshold system, treelike version [missing?] Res(L\(\&\)P) with unary coefficients
• Semantic degree-k threshold system, treelike version [missing?] Polynomial Calculus over \(\mathbb{F}_2\)
• Semantic degree-k threshold system, treelike version [missing?] Nullstellensatz over \(\mathbb{F}_2\)
• Semantic degree-k threshold system, treelike version [missing?] ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals
• Semantic degree-k threshold system, treelike version [missing?] unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals
• Semantic degree-k threshold system, treelike version [missing?] ResLin over \(\mathbb{F}_2\), Res(\(\oplus\))
• Semantic degree-k threshold system, treelike version [missing?] Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\))
• Semantic degree-k threshold system, treelike version [missing?] Polynomial Calculus over \(\mathbb{Q}\)
• Semantic degree-k threshold system, treelike version [missing?] Nullstellensatz over \(\mathbb{Q}\)
• Semantic degree-k threshold system, treelike version simulates Hitting
• Source: tlTH(k) → tlCP → tlRes → hit
• Semantic degree-k threshold system, treelike version [missing?] Lift and Project
• Semantic degree-k threshold system, treelike version [missing?] Lift and Project with unary coefficients
• Semantic degree-k threshold system, treelike version [missing?] Positivstellensatz Calculus
• Semantic degree-k threshold system, treelike version [missing?] Positivstellensatz
• Semantic degree-k threshold system, treelike version [missing?] Lovász--Schrijver (LS)
• Semantic degree-k threshold system, treelike version [missing?] Lovász--Schrijver with squares (LS\(_+\))
• Semantic degree-k threshold system, treelike version [missing?] Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree
• Semantic degree-k threshold system, treelike version [missing?] Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree
• Semantic degree-k threshold system, treelike version [missing?] Cone Proof System
• Semantic degree-k threshold system, treelike version simulates tl Lovász--Schrijver (LS)
• Source: tlTH(k) → tlLSd+ → tlLS+ → tlLS
• Semantic degree-k threshold system, treelike version simulates Lovász--Schrijver with squares (LS\(_+\))
• Source: tlTH(k) → tlLSd+ → tlLS+
• Semantic degree-k threshold system, treelike version simulates Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike
• Source: [subsystem]
• Semantic degree-k threshold system, treelike version [missing?] static Lovász--Schrijver (static LS)
• Semantic degree-k threshold system, treelike version [missing?] static Lovász--Schrijver, with squares of linear functions (static LS\(_+\))
• Semantic degree-k threshold system, treelike version [missing?] static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\))
• Semantic degree-k threshold system, treelike version [missing?] Sum of Squares (Lasserre)
• Semantic degree-k threshold system, treelike version [missing?] Sherali--Adams
• Semantic degree-k threshold system, treelike version [missing?] Circular resolution
• Semantic degree-k threshold system, treelike version [missing?] Unary Sherali--Adams
• Semantic degree-k threshold system, treelike version [missing?] Ideal Proof System
• Semantic degree-k threshold system, treelike version [missing?] Extended Frege
• Semantic degree-k threshold system, treelike version [missing?] Extended resolution
• Semantic degree-k threshold system, treelike version [missing?] Frege
• Semantic degree-k threshold system, treelike version [missing?] \(\mathrm{AC}^0\)-Frege
• Semantic degree-k threshold system, treelike version [missing?] k-DNF Resolution
• Semantic degree-k threshold system, treelike version [missing?] \(\mathrm{TC}^0\)-Frege
• Semantic degree-k threshold system, treelike version [missing?] \(\mathrm{AC}^0\)-Frege with mod 2 axioms
• Semantic degree-k threshold system, treelike version [missing?] \(\mathrm{AC}^0\)-Frege with mod 2 gates
• Semantic degree-k threshold system, treelike version [missing?] OBDD(join,weakening)
• Semantic degree-k threshold system, treelike version [missing?] LK
• Semantic degree-k threshold system, treelike version [missing?] Zermelo-Fraenkl Set Theory with the Axiom of Choice

Formulas

• The size complexity of Pigeonhole principle in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Pigeonhole principle with functionality axioms in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Pigeonhole principle with functionality and onto axioms in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Weak pigeonhole principle (2n pigeons, n holes) in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Bitwise pigeonhole principle in Semantic degree-k threshold system, treelike version is exponential
• Source: IR21 Proof Complexity of Natural Formulas via Communication Arguments.
• The size complexity of Relativized pigeonhole principle (n,\(n^2\),n-1) in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Ordering principle in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Guarded ordering principle in Semantic degree-k threshold system, treelike version is [missing?]
• 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 \(\mathbb{F}_2\) with k-ary AND gadget in Semantic degree-k threshold system, treelike version is exponential
• Source: BeamePS07 Lower Bounds for Lov[a-acute]sz--Schrijver Systems and Beyond Follow from Multiparty Communication Complexity.
• The size complexity of Tseitin over \(\mathbb{Q}\) in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Flow in Semantic degree-k threshold system, treelike version 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 \(\mathbb{Q}\) \(\circ\) IND in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Random CNF in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Clique-Colouring in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Weak Clique-Colouring (m^1/2 clique, log^2 m colours) in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Clique-Colouring composed with a permutation in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Pebbling \(\circ\) IND in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Pebbling \(\circ\) XOR, then guarded in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Stone formula in Semantic degree-k threshold system, treelike version is [missing?]
• 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 Sink of DAG \(\circ\) XOR in Semantic degree-k threshold system, treelike version 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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