Refutation Of Hard-Determinable Formulas In The System “Resolution Over Linear Equations” And Its Generalization
Pure and Applied Mathematics Journal
Volume 2, Issue 3, June 2013, Pages: 128-133
Received: May 11, 2013;
Published: Jun. 20, 2013
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Anahit Chubaryan, Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, Armenia
Armine Chubaryan, Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, Armenia
Arman Tshitoyan, Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, Armenia
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We research the power of the propositional proof system R(lin) (Resolution over Linear Equations) described by Ran Raz and Iddo Tzameret. R (lin) is the generalization of R (Resolution System) and it is known that many tautologies, which require the exponential lower bounds of proof complexities in R, have polynomially bounded proofs in R (lin). We show that there are the sequences of unsatisfiable collections of disjuncts of linear equations, which require exponential lower bounds in R (lin). After adding the renaming rule, mentioned collections have polynomially bounded refutations.
Resolution Systems, Resolution over Linear Equations, Refutation, Proof Complexity, Hard-Determinable Formula
To cite this article
Refutation Of Hard-Determinable Formulas In The System “Resolution Over Linear Equations” And Its Generalization, Pure and Applied Mathematics Journal.
Vol. 2, No. 3,
2013, pp. 128-133.
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