All about Unary Sherali--Adams

Proof Systems

• Unary Sherali--Adams does not simulate Resolution
• Source: Res → sod+xor → uSA
• Unary Sherali--Adams simulates Truth table
• Source: uSA → revRes → tlRes → ttp
• Unary Sherali--Adams simulates Tree-like resolution
• Source: uSA → revRes → tlRes
• Unary Sherali--Adams [missing?] Regular resolution
• Unary Sherali--Adams not simulated by Ordered resolution
• Source: uSA → revRes → tlRes → pearl → ordRes
• Unary Sherali--Adams [missing?] Pool resolution
• Unary Sherali--Adams [missing?] Linear resolution
• Unary Sherali--Adams simulates Reversible resolution
• Source: [citation needed]
• Unary Sherali--Adams does not simulate Cutting Planes
• Source: CP → uCP → Res → sod+xor → uSA
• Unary Sherali--Adams [missing?] Tree-like Cutting Planes
• Unary Sherali--Adams does not simulate Cutting Planes with Unary Coefficients
• Source: uCP → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Semantic Cutting Planes
• Source: semanticCP → saturationCP → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Cutting Planes with Saturation
• Source: saturationCP → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Stabbing Planes
• Source: SP → uSP → uCP → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Stabbing Planes with Unary Coefficients
• Source: uSP → uCP → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Res(CP)
• Source: Res(CP) → CP → uCP → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Res(LP)
• Source: Res(LP) → uRes(LP) → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Res(CP) with unary coefficients
• Source: uRes(CP) → uCP → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Res(LP) with unary coefficients
• Source: uRes(LP) → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Res(L\(\&\)P)
• Source: Res(L&P) → Res(LP) → uRes(LP) → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Res(L\(\&\)P) with unary coefficients
• Source: uRes(L&P) → uRes(LP) → Res → sod+xor → uSA
• Unary Sherali--Adams [missing?] Semantic degree-k threshold system, treelike version
• Unary Sherali--Adams does not simulate Polynomial Calculus over \(\mathbb{F}_2\)
• Source: PC_F2 → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Nullstellensatz over \(\mathbb{F}_2\)
• Source: NS_F2 → tseitin → SoS → SA → uSA
• Unary Sherali--Adams does not simulate ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals
• Source: ResLin_Z → uResLin_Z → ResLin_F2 → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals
• Source: uResLin_Z → ResLin_F2 → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate ResLin over \(\mathbb{F}_2\), Res(\(\oplus\))
• Source: ResLin_F2 → Res → sod+xor → uSA
• Unary Sherali--Adams [missing?] Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\))
• Unary Sherali--Adams does not simulate Polynomial Calculus over \(\mathbb{Q}\)
• Source: PC_Q → Res → sod+xor → uSA
• Unary Sherali--Adams [missing?] Nullstellensatz over \(\mathbb{Q}\)
• Unary Sherali--Adams simulates Hitting
• Source: uSA → revRes → tlRes → hit
• Unary Sherali--Adams does not simulate Lift and Project
• Source: L&P → uL&P → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Lift and Project with unary coefficients
• Source: uL&P → Res → sod+xor → uSA
• Unary Sherali--Adams weaker than Positivstellensatz Calculus
• Source: PSC → PS → SoS → SA → uSA
• Source: PSC → PS → SoS → PC_Q → Res → sod+xor → uSA
• Unary Sherali--Adams weaker than Positivstellensatz
• Source: PS → SoS → SA → uSA
• Source: PS → SoS → PC_Q → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Lovász--Schrijver (LS)
• Source: LS → L&P → uL&P → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Lovász--Schrijver with squares (LS\(_+\))
• Source: LS+ → LS → L&P → uL&P → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree
• Source: LSd+ → tseitin → SoS → SA → uSA
• Unary Sherali--Adams weaker than Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree
• Source: LSn+ → PSC → PS → SoS → SA → uSA
• Source: LSn+ → LSd+ → tseitin → SoS → SA → uSA
• Unary Sherali--Adams weaker than Cone Proof System
• Source: CPS → LSn+ → PSC → PS → SoS → SA → uSA
• Source: CPS → LSn+ → LSd+ → tseitin → SoS → SA → uSA
• Unary Sherali--Adams [missing?] tl Lovász--Schrijver (LS)
• Unary Sherali--Adams [missing?] Lovász--Schrijver with squares (LS\(_+\))
• Unary Sherali--Adams [missing?] Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike
• Unary Sherali--Adams [missing?] static Lovász--Schrijver (static LS)
• Unary Sherali--Adams [missing?] static Lovász--Schrijver, with squares of linear functions (static LS\(_+\))
• Unary Sherali--Adams [missing?] static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\))
• Unary Sherali--Adams weaker than Sum of Squares (Lasserre)
• Source: SoS → SA → uSA
• Source: SoS → PC_Q → Res → sod+xor → uSA
• Unary Sherali--Adams weaker than Sherali--Adams
• Source: [subsystem]
• Source: SA → circRes → Res → sod+xor → uSA
• Unary Sherali--Adams weaker than Circular resolution
• Source: circRes → SA → uSA
• Source: circRes → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Ideal Proof System
• Source: IPS → extFrege → extRes → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Extended Frege
• Source: extFrege → extRes → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Extended resolution
• Source: extRes → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Frege
• Source: Frege → AC0Frege → Res-k → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate \(\mathrm{AC}^0\)-Frege
• Source: AC0Frege → Res-k → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate k-DNF Resolution
• Source: Res-k → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate \(\mathrm{TC}^0\)-Frege
• Source: TC0Frege → AC0Frege → Res-k → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate \(\mathrm{AC}^0\)-Frege with mod 2 axioms
• Source: AC0Frege+Mod2axioms → AC0Frege → Res-k → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate \(\mathrm{AC}^0\)-Frege with mod 2 gates
• Source: AC0(+)Frege → ResLin_F2 → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate OBDD(join,weakening)
• Source: OBDDjoinweak → uCP → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate LK
• Source: LK → Frege → AC0Frege → Res-k → Res → sod+xor → uSA
• Unary Sherali--Adams does not simulate Zermelo-Fraenkl Set Theory with the Axiom of Choice
• Source: ZFC → extFrege → extRes → Res → sod+xor → uSA

Formulas

• The size complexity of Pigeonhole principle in Unary Sherali--Adams is [missing?]
• The size complexity of Pigeonhole principle with functionality axioms in Unary Sherali--Adams is [missing?]
• The size complexity of Pigeonhole principle with functionality and onto axioms in Unary Sherali--Adams is [missing?]
• The size complexity of Weak pigeonhole principle (2n pigeons, n holes) in Unary Sherali--Adams is [missing?]
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Unary Sherali--Adams is [missing?]
• The size complexity of Bitwise pigeonhole principle in Unary Sherali--Adams is [missing?]
• The size complexity of Relativized pigeonhole principle (n,\(n^2\),n-1) in Unary Sherali--Adams is exponential
• Source: rPHP → SA → uSA
• The size complexity of Ordering principle in Unary Sherali--Adams is [missing?]
• The size complexity of Guarded ordering principle in Unary Sherali--Adams is [missing?]
• 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 \(\mathbb{F}_2\) with k-ary AND gadget in Unary Sherali--Adams is [missing?]
• The size complexity of Tseitin over \(\mathbb{Q}\) in Unary Sherali--Adams is [missing?]
• The size complexity of Flow in Unary Sherali--Adams is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Unary Sherali--Adams is [missing?]
• The size complexity of Tseitin \(\mathbb{Q}\) \(\circ\) IND in Unary Sherali--Adams is [missing?]
• The size complexity of Random CNF in Unary Sherali--Adams is [missing?]
• The size complexity of Clique-Colouring in Unary Sherali--Adams is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Unary Sherali--Adams is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Unary Sherali--Adams is [missing?]
• The size complexity of Weak Clique-Colouring (m^1/2 clique, log^2 m colours) in Unary Sherali--Adams is [missing?]
• The size complexity of Clique-Colouring composed with a permutation in Unary Sherali--Adams is [missing?]
• The size complexity of Pebbling \(\circ\) IND in Unary Sherali--Adams is [missing?]
• The size complexity of Pebbling \(\circ\) XOR, then guarded in Unary Sherali--Adams is [missing?]
• The size complexity of Stone formula in Unary Sherali--Adams is [missing?]
• The size complexity of String of pearls in Unary Sherali--Adams is at most quasipolynomial
• Source: uSA → revRes → tlRes → pearl
• The size complexity of Sink of DAG \(\circ\) XOR in Unary Sherali--Adams is exponential
• Source: GHJMPRT22 Separations in Proof Complexity and TFNP.

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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