TY - GEN
T1 - The Power of the Binary Value Principle
AU - Alekseev, Yaroslav
AU - Hirsch, Edward A.
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023
Y1 - 2023
N2 - The (extended) Binary Value Principle(formula presented) and in the presence of has received a lot of attention recently, several lower bounds have been proved for it [1, 2, 10]. It has been shown [2] that the probabilistically verifiable Ideal Proof System [8] together with polynomially simulates a similar semialgebraic proof system. In this paper we consider Polynomial Calculus with the algebraic version of Tseitin’s extension rule(formula presented), this is a Cook–Reckhow proof system. We show that in this context still allows to simulate similar semialgebraic systems. We also prove that it allows to simulate the Square Root Rule [6] in a sharp contrast to the result of [1] that shows an exponential lower bound on the size of (formula presented) from its square. On the other hand, we demonstrate that probably does not help in proving exponential lower bounds for Boolean formulas: we show that an (formula presented) (even with the Square Root Rule) derivation of any unsatisfiable Boolean formula in CNF from must be of exponential size.
AB - The (extended) Binary Value Principle(formula presented) and in the presence of has received a lot of attention recently, several lower bounds have been proved for it [1, 2, 10]. It has been shown [2] that the probabilistically verifiable Ideal Proof System [8] together with polynomially simulates a similar semialgebraic proof system. In this paper we consider Polynomial Calculus with the algebraic version of Tseitin’s extension rule(formula presented), this is a Cook–Reckhow proof system. We show that in this context still allows to simulate similar semialgebraic systems. We also prove that it allows to simulate the Square Root Rule [6] in a sharp contrast to the result of [1] that shows an exponential lower bound on the size of (formula presented) from its square. On the other hand, we demonstrate that probably does not help in proving exponential lower bounds for Boolean formulas: we show that an (formula presented) (even with the Square Root Rule) derivation of any unsatisfiable Boolean formula in CNF from must be of exponential size.
KW - Extension Rule
KW - Polynomial Calculus
KW - Proof complexity
UR - http://www.scopus.com/inward/record.url?scp=85161384651&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-30448-4_3
DO - 10.1007/978-3-031-30448-4_3
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AN - SCOPUS:85161384651
SN - 9783031304477
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 21
EP - 36
BT - Algorithms and Complexity - 13th International Conference, CIAC 2023, Proceedings
A2 - Mavronicolas, Marios
PB - Springer Science and Business Media Deutschland GmbH
T2 - 13th International Symposium on Algorithms and Complexity, CIAC 2023
Y2 - 13 June 2023 through 16 June 2023
ER -