All about Circular resolution

Proof Systems

• Circular resolution stronger than Resolution
• Source: [subsystem]
• Source: circRes → SA → NS_Q → ofPHP → Res
• Circular resolution stronger than Truth table
• Source: circRes → Res → regRes → tlRes → ttp
• Source: circRes → Res → regRes → ordering → tlRes → ttp
• Circular resolution stronger than Tree-like resolution
• Source: circRes → Res → regRes → tlRes
• Source: circRes → Res → regRes → ordering → tlRes
• Circular resolution stronger than Regular resolution
• Source: circRes → Res → regRes
• Source: circRes → Res → poolRes → stone → regRes
• Circular resolution stronger than Ordered resolution
• Source: circRes → Res → regRes → ordRes
• Source: circRes → Res → regRes → pearl → ordRes
• Circular resolution stronger than Pool resolution
• Source: circRes → Res → poolRes
• Source: circRes → SA → NS_Q → ofPHP → Res → poolRes
• Circular resolution stronger than Linear resolution
• Source: circRes → Res → linRes
• Source: circRes → SA → NS_Q → ofPHP → Res → linRes
• Circular resolution stronger than Reversible resolution
• Source: circRes → Res → revRes
• Source: circRes → Res → sod+xor → uSA → revRes
• Circular resolution incomparable wrt Cutting Planes
• Source: circRes → SA → NS_Q → tsQ+ind → CP
• Source: CP → tseitin → SoS → SA → circRes
• Circular resolution not simulated by Tree-like Cutting Planes
• Source: circRes → Res → regRes → ordRes → peb+ind → tlCP
• Circular resolution not simulated by Cutting Planes with Unary Coefficients
• Source: circRes → SA → NS_Q → tsQ+ind → CP → uCP
• Circular resolution does not simulate Semantic Cutting Planes
• Source: semanticCP → CP → tseitin → SoS → SA → circRes
• Circular resolution stronger than Cutting Planes with Saturation
• Source: circRes → Res → saturationCP
• Source: circRes → SA → NS_Q → ofPHP → Res → saturationCP
• Circular resolution does not simulate Stabbing Planes
• Source: SP → tseitin → SoS → SA → circRes
• Circular resolution not simulated by Stabbing Planes with Unary Coefficients
• Source: circRes → SA → NS_Q → tsQ+ind → CP → uSP
• Circular resolution does not simulate Res(CP)
• Source: Res(CP) → Res(LP) → uRes(LP) → tseitin → SoS → SA → circRes
• Circular resolution does not simulate Res(LP)
• Source: Res(LP) → uRes(LP) → tseitin → SoS → SA → circRes
• Circular resolution does not simulate Res(CP) with unary coefficients
• Source: uRes(CP) → uRes(LP) → tseitin → SoS → SA → circRes
• Circular resolution does not simulate Res(LP) with unary coefficients
• Source: uRes(LP) → tseitin → SoS → SA → circRes
• Circular resolution does not simulate Res(L\(\&\)P)
• Source: Res(L&P) → Res(LP) → uRes(LP) → tseitin → SoS → SA → circRes
• Circular resolution does not simulate Res(L\(\&\)P) with unary coefficients
• Source: uRes(L&P) → uRes(LP) → tseitin → SoS → SA → circRes
• Circular resolution [missing?] Semantic degree-k threshold system, treelike version
• Circular resolution incomparable wrt Polynomial Calculus over \(\mathbb{F}_2\)
• Source: circRes → SA → PHP → PC_F2
• Source: PC_F2 → NS_F2 → tseitin → SoS → SA → circRes
• Circular resolution incomparable wrt Nullstellensatz over \(\mathbb{F}_2\)
• Source: circRes → SA → PHP → PC_F2 → NS_F2
• Source: NS_F2 → tseitin → SoS → SA → circRes
• Circular resolution does not simulate ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals
• Source: ResLin_Z → uResLin_Z → ResLin_F2 → tseitin → SoS → SA → circRes
• Circular resolution does not simulate unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals
• Source: uResLin_Z → ResLin_F2 → tseitin → SoS → SA → circRes
• Circular resolution does not simulate ResLin over \(\mathbb{F}_2\), Res(\(\oplus\))
• Source: ResLin_F2 → tseitin → SoS → SA → circRes
• Circular resolution not simulated by Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\))
• Source: circRes → SA → PHP → tlResLin_F2
• Circular resolution not simulated by Polynomial Calculus over \(\mathbb{Q}\)
• Source: circRes → SA → PHP → PC_Q
• Circular resolution stronger than Nullstellensatz over \(\mathbb{Q}\)
• Source: circRes → SA → NS_Q
• Source: circRes → SA → PHP → PC_Q → NS_Q
• Circular resolution stronger than Hitting
• Source: circRes → Res → regRes → tlRes → hit
• Source: circRes → Res → regRes → ordering → tlRes → hit
• Circular resolution [missing?] Lift and Project
• Circular resolution not simulated by Lift and Project with unary coefficients
• Source: circRes → SA → NS_Q → tsQ+ind → CP → uCP → uL&P
• Circular resolution simulated by Positivstellensatz Calculus
• Source: PSC → PS → SoS → SA → circRes
• Circular resolution simulated by Positivstellensatz
• Source: PS → SoS → SA → circRes
• Circular resolution [missing?] Lovász--Schrijver (LS)
• Circular resolution [missing?] Lovász--Schrijver with squares (LS\(_+\))
• Circular resolution does not simulate Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree
• Source: LSd+ → tseitin → SoS → SA → circRes
• Circular resolution weaker than Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree
• Source: LSn+ → PSC → PS → SoS → SA → circRes
• Source: LSn+ → LSd+ → tseitin → SoS → SA → circRes
• Circular resolution weaker than Cone Proof System
• Source: CPS → LSn+ → PSC → PS → SoS → SA → circRes
• Source: CPS → LSn+ → LSd+ → tseitin → SoS → SA → circRes
• Circular resolution [missing?] tl Lovász--Schrijver (LS)
• Circular resolution [missing?] Lovász--Schrijver with squares (LS\(_+\))
• Circular resolution [missing?] Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike
• Circular resolution [missing?] static Lovász--Schrijver (static LS)
• Circular resolution [missing?] static Lovász--Schrijver, with squares of linear functions (static LS\(_+\))
• Circular resolution [missing?] static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\))
• Circular resolution simulated by Sum of Squares (Lasserre)
• Source: SoS → SA → circRes
• Circular resolution equivalent Sherali--Adams
• Source: AL19 Circular (Yet Sound) Proofs.
• Circular resolution stronger than Unary Sherali--Adams
• Source: circRes → SA → uSA
• Source: circRes → Res → sod+xor → uSA
• Circular resolution does not simulate Ideal Proof System
• Source: IPS → extFrege → Frege → AC0(+)Frege → ResLin_F2 → tseitin → SoS → SA → circRes
• Circular resolution does not simulate Extended Frege
• Source: extFrege → Frege → AC0(+)Frege → ResLin_F2 → tseitin → SoS → SA → circRes
• Circular resolution does not simulate Extended resolution
• Source: extRes → extFrege → Frege → AC0(+)Frege → ResLin_F2 → tseitin → SoS → SA → circRes
• Circular resolution does not simulate Frege
• Source: Frege → AC0(+)Frege → ResLin_F2 → tseitin → SoS → SA → circRes
• Circular resolution not simulated by \(\mathrm{AC}^0\)-Frege
• Source: circRes → SA → NS_Q → ofPHP → AC0Frege
• Circular resolution not simulated by k-DNF Resolution
• Source: circRes → SA → NS_Q → ofPHP → AC0Frege → Res-k
• Circular resolution does not simulate \(\mathrm{TC}^0\)-Frege
• Source: TC0Frege → Res(CP) → Res(LP) → uRes(LP) → tseitin → SoS → SA → circRes
• Circular resolution does not simulate \(\mathrm{AC}^0\)-Frege with mod 2 axioms
• Source: AC0Frege+Mod2axioms → NS_F2 → tseitin → SoS → SA → circRes
• Circular resolution does not simulate \(\mathrm{AC}^0\)-Frege with mod 2 gates
• Source: AC0(+)Frege → ResLin_F2 → tseitin → SoS → SA → circRes
• Circular resolution does not simulate OBDD(join,weakening)
• Source: OBDDjoinweak → tseitin → SoS → SA → circRes
• Circular resolution does not simulate LK
• Source: LK → Frege → AC0(+)Frege → ResLin_F2 → tseitin → SoS → SA → circRes
• Circular resolution does not simulate Zermelo-Fraenkl Set Theory with the Axiom of Choice
• Source: ZFC → Res(CP) → Res(LP) → uRes(LP) → tseitin → SoS → SA → circRes

Formulas

• The size complexity of Pigeonhole principle in Circular resolution is polynomial
• Source: circRes → SA → PHP
• The size complexity of Pigeonhole principle with functionality axioms in Circular resolution is polynomial
• Source: circRes → SA → PHP → fPHP
• The size complexity of Pigeonhole principle with functionality and onto axioms in Circular resolution is polynomial
• Source: circRes → SA → NS_Q → ofPHP
• The size complexity of Weak pigeonhole principle (2n pigeons, n holes) in Circular resolution is polynomial
• Source: circRes → SA → PHP → PHP2nn
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in Circular resolution is polynomial
• Source: circRes → SA → PHP → PHP2nn → PHPn2n
• The size complexity of Bitwise pigeonhole principle in Circular resolution is [missing?]
• The size complexity of Relativized pigeonhole principle (n,\(n^2\),n-1) in Circular resolution is exponential
• Source: rPHP → SA → circRes
• The size complexity of Ordering principle in Circular resolution is polynomial
• Source: circRes → Res → regRes → ordering
• The size complexity of Guarded ordering principle in Circular resolution is polynomial
• Source: circRes → Res → poolRes → ordering+guard
• 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 \(\mathbb{F}_2\) with k-ary AND gadget in Circular resolution is [missing?]
• The size complexity of Tseitin over \(\mathbb{Q}\) in Circular resolution is polynomial
• Source: circRes → SA → NS_Q → tseitinQ
• The size complexity of Flow in Circular resolution is [missing?]
• The size complexity of Tseitin \(\mathbb{F}_2\) \(\circ\) IND in Circular resolution is [missing?]
• The size complexity of Tseitin \(\mathbb{Q}\) \(\circ\) IND in Circular resolution is at most quasipolynomial
• Source: circRes → SA → NS_Q → tsQ+ind
• The size complexity of Random CNF in Circular resolution is [missing?]
• The size complexity of Clique-Colouring in Circular resolution is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Circular resolution is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in Circular resolution is [missing?]
• The size complexity of Weak Clique-Colouring (m^1/2 clique, log^2 m colours) in Circular resolution is [missing?]
• The size complexity of Clique-Colouring composed with a permutation in Circular resolution is [missing?]
• The size complexity of Pebbling \(\circ\) IND in Circular resolution is polynomial
• Source: circRes → Res → regRes → ordRes → peb+ind
• The size complexity of Pebbling \(\circ\) XOR, then guarded in Circular resolution is polynomial
• Source: circRes → Res → poolRes → peb+xor+guard
• The size complexity of Stone formula in Circular resolution is polynomial
• Source: circRes → Res → poolRes → stone
• The size complexity of String of pearls in Circular resolution is polynomial
• Source: circRes → Res → regRes → pearl
• The size complexity of Sink of DAG \(\circ\) XOR in Circular resolution is polynomial
• Source: circRes → Res → sod+xor

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.

Licensed under CC BY 4.0