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Electronic Colloquium on Computational Complexity

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Reports tagged with Nullstellensatz refutations:
TR16-101 | 1st July 2016
Toniann Pitassi, Iddo Tzameret

Algebraic Proof Complexity: Progress, Frontiers and Challenges

We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to old problems, and new directions of research. In particular, we focus on tight ... more >>>

TR19-186 | 31st December 2019
Or Meir, Jakob Nordström, Toniann Pitassi, Robert Robere, Susanna de Rezende

Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity

Revisions: 4

We significantly strengthen and generalize the theorem lifting Nullstellensatz degree to monotone span program size by Pitassi and Robere (2018) so that it works for any gadget with high enough rank, in particular, for useful gadgets such as equality and greater-than. We apply our generalized theorem to solve two open ... more >>>

TR20-001 | 31st December 2019
Or Meir, Jakob Nordström, Robert Robere, Susanna de Rezende

Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling

Revisions: 2

We establish an exactly tight relation between reversible pebblings of graphs and Nullstellensatz refutations of pebbling formulas, showing that a graph $G$ can be reversibly pebbled in time $t$ and space $s$ if and only if there is a Nullstellensatz refutation of the pebbling formula over $G$ in size $t+1$ ... more >>>

TR24-072 | 11th April 2024
Yaroslav Alekseev, Dima Grigoriev, Edward Hirsch

Tropical proof systems

Propositional proof complexity deals with the lengths of polynomial-time verifiable proofs for Boolean tautologies. An abundance of proof systems is known, including algebraic and semialgebraic systems, which work with polynomial equations and inequalities, respectively. The most basic algebraic proof system is based on Hilbert's Nullstellensatz (Beame et al., 1996). Tropical ... more >>>

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