Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Algebraic proof systems, such as Polynomial Calculus (PC) and Polynomial Calculus with Resolution (PCR), refute contradictions using polynomials. Space complexity for such systems measures the number of distinct monomials to be kept in memory while verifying a proof.  introduce a new combinatorial framework for proving space lor bounds in algebraic proof systems. As an immediate application,  obtain the space lor bounds previously provided for PC/PCR [Alekhnovich et al. 2002; Filmus et al. 2012]. More importantly, using our approach in its full potential,  prove Ω( n ) space lor bounds in PC/PCR for random  k -CNFs ( k ≥ 4) in  n  variables, thus solving an open problem posed in Alekhnovich et al. [2002] and Filmus et al. [2012]. Our method also applies to the Graph Pigeonhole Principle, which is a variant of the Pigeonhole Principle defined over a constant (left) degree expander graph.
['Ilario Bonacina', 'Nicola Galesi']
I am writing a research paper on a idea A Framework for Space Complexity in Algebraic Proof Systems
[{"from": "human", "value": "I am writing a research paper on a idea A Framework for Space Complexity in Algebraic Proof Systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Algebraic proof systems, such as Polynomial Calculus (PC) and Polynomial Calculus with Resolution (PCR), refute contradictions using polynomials. Space complexity for such systems measures the number of distinct monomials to be kept in memory while verifying a proof.  introduce a new combinatorial framework for proving space lor bounds in algebraic proof systems. As an immediate application,  obtain the space lor bounds previously provided for PC/PCR [Alekhnovich et al. 2002; Filmus et al. 2012]. More importantly, using our approach in its full potential,  prove \u03a9( n ) space lor bounds in PC/PCR for random  k -CNFs ( k \u2265 4) in  n  variables, thus solving an open problem posed in Alekhnovich et al. [2002] and Filmus et al. [2012]. Our method also applies to the Graph Pigeonhole Principle, which is a variant of the Pigeonhole Principle defined over a constant (left) degree expander graph."}]