The Power of the Binary Value Principle

Yaroslav Alekseev, Edward A. Hirsch

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationAlgorithms and Complexity - 13th International Conference, CIAC 2023, Proceedings
EditorsMarios Mavronicolas
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages16
ISBN (Print)9783031304477
StatePublished - 2023
Externally publishedYes
Event13th International Symposium on Algorithms and Complexity, CIAC 2023 - Larnaca, Cyprus
Duration: 13 Jun 202316 Jun 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13898 LNCS


Conference13th International Symposium on Algorithms and Complexity, CIAC 2023


  • Extension Rule
  • Polynomial Calculus
  • Proof complexity

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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