  Under the auspices of the Computational Complexity Foundation (CCF)     REPORTS > KEYWORD > RESOLUTION OVER LINEAR EQUATIONS:
Reports tagged with Resolution over linear equations:
TR17-117 | 20th July 2017
Dmitry Itsykson, Alexander Knop

#### Hard satisfiable formulas for splittings by linear combinations

Itsykson and Sokolov in 2014 introduced the class of DPLL($\oplus$) algorithms that solve Boolean satisfiability problem using the splitting by linear combinations of variables modulo 2. This class extends the class of DPLL algorithms that split by variables. DPLL($\oplus$) algorithms solve in polynomial time systems of linear equations modulo two ... more >>>

TR18-117 | 23rd June 2018
Fedor Part, Iddo Tzameret

#### Resolution with Counting: Lower Bounds over Different Moduli

Revisions: 2

Resolution over linear equations (introduced in [RT08]) emerged recently as an important object of study. This refutation system, denoted Res(lin$_R$), operates with disjunction of linear equations over a ring $R$. On the one hand, the system captures a natural minimal'' extension of resolution in which efficient counting can be achieved; ... more >>>

TR20-034 | 12th March 2020
Erfan Khaniki

#### On Proof complexity of Resolution over Polynomial Calculus

Revisions: 3

The refutation system ${Res}_R({PC}_d)$ is a natural extension of resolution refutation system such that it operates with disjunctions of degree $d$ polynomials over ring $R$ with boolean variables. For $d=1$, this system is called ${Res}_R({lin})$. Based on properties of $R$, ${Res}_R({lin})$ systems can be too strong to prove lower ... more >>>

TR20-184 | 10th December 2020
Dmitry Itsykson, Artur Riazanov

#### Proof complexity of natural formulas via communication arguments

A canonical communication problem ${\rm Search}(\phi)$ is defined for every unsatisfiable CNF $\phi$: an assignment to the variables of $\phi$ is distributed among the communicating parties, they are to find a clause of $\phi$ falsified by this assignment. Lower bounds on the randomized $k$-party communication complexity of ${\rm Search}(\phi)$ in ... more >>>

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