All about ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals

Definition from: Resolution over linear equations and multilinear proofs.

Proof Systems

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

Formulas

• The size complexity of Pigeonhole principle in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → uRes(CP) → uCP → PHP
• The size complexity of Pigeonhole principle with functionality axioms in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → uRes(CP) → uCP → PHP → fPHP
• The size complexity of Pigeonhole principle with functionality and onto axioms in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → uRes(CP) → uCP → PHP → fPHP → ofPHP
• The size complexity of Weak pigeonhole principle (2n pigeons, n holes) in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → uRes(CP) → uCP → PHP → PHP2nn
• The size complexity of Weak pigeonhole principle (\(n^2\) pigeons, n holes) in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → uRes(CP) → uCP → PHP → PHP2nn → PHPn2n
• The size complexity of Bitwise pigeonhole principle in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Relativized pigeonhole principle (n,\(n^2\),n-1) in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Ordering principle in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → ResLin_F2 → Res → regRes → ordering
• The size complexity of Guarded ordering principle in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → ResLin_F2 → Res → poolRes → ordering+guard
• 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 \(\mathbb{F}_2\) with k-ary AND gadget in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Tseitin over \(\mathbb{Q}\) in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Flow 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 ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Tseitin \(\mathbb{Q}\) \(\circ\) IND in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Random CNF in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Clique-Colouring in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Weak Clique-Colouring (2m clique, m colours) in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Weak Clique-Colouring (m^1/2 clique, log^2 m colours) in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → uRes(CP) → uRes(LP) → Res-k → CliqueColouringmlogm
• The size complexity of Clique-Colouring composed with a permutation in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Pebbling \(\circ\) IND in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → ResLin_F2 → Res → regRes → ordRes → peb+ind
• The size complexity of Pebbling \(\circ\) XOR, then guarded in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → ResLin_F2 → Res → poolRes → peb+xor+guard
• The size complexity of Stone formula in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → ResLin_F2 → Res → poolRes → stone
• The size complexity of String of pearls in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → ResLin_F2 → Res → regRes → pearl
• The size complexity of Sink of DAG \(\circ\) XOR in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is polynomial
• Source: ResLin_Z → uResLin_Z → ResLin_F2 → 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.

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