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- Albert Atserias, Nicola Galesi, Pavel Pudlák
- IEEE Conference on Computational Complexity
- 2001

We show that an LK proof of size m of a monotone sequent (a sequent that contains only formulas in the basis ^; _) can be turned into a proof containing only monotone formulas of size m O(logm) and with the number of proof lines polynomial in m. Also we show that some interesting special cases, namely the functional and the onto versions of PHP and a… (More)

- Maria Luisa Bonet, Juan Luis Esteban, Nicola Galesi, Jan Johannsen
- SIAM J. Comput.
- 2000

An exponential lower bound for the size of tree-like Cutting Planes refutations of a certain family of CN F formulas with polynomial size resolution refutations is proved. This implies an exponential separation between the tree-like versions and the dag-like versions of resolution and Cutting Planes. In both cases only superpolynomial separations were known… (More)

- Joshua Buresh-Oppenheim, Nicola Galesi, Shlomo Hoory, Avner Magen, Toniann Pitassi
- Theory of Computing
- 2003

We present a new method for proving rank lower bounds for the cutting planes procedures of Gomory and Chvátal (GC) and Lovász and Schrijver (LS), when viewed as proof systems for unsatisfiability. We apply this method to obtain the following new results: First, we prove near-optimal rank bounds for GC and LS proofs for several prominent unsatisfiable CNF… (More)

- Eli Ben-Sasson, Nicola Galesi
- Electronic Colloquium on Computational Complexity
- 2001

Proofs of computational effort were devised to control denial of service attacks. Dwork and Naor (CRYPTO '92), for example, proposed to use such proofs to discourage spam. The idea is to couple each email message with a proof of work that demonstrates the sender performed some computational task. A proof of work can be either CPU-bound or memory-bound. In a… (More)

- Ilario Bonacina, Nicola Galesi
- Electronic Colloquium on Computational Complexity
- 2012

We devise a new combinatorial framework for proving space lower bounds in algebraic proof systems like Polynomial Calculus (Pc) and Polynomial Calculus with Resolution (Pcr). Our method can be thought as a Spoiler-Duplicator game, which is capturing boolean reasoning on polynomials instead that clauses as in the case of Resolution. Hence, for the first… (More)

- Olaf Beyersdorff, Nicola Galesi, Massimo Lauria
- Circuits, Logic, and Games
- 2010

ter for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The rst section describes the seminar topics and goals in general. Links… (More)

- Nicola Galesi, Pavel Pudlák, Neil Thapen
- Electronic Colloquium on Computational Complexity
- 2014

We study the space complexity of the cutting planes proof system, in which the lines in a proof are integral linear inequalities. We measure the space used by a refutation as the number of linear inequalities that need to be kept on a blackboard while verifying it. We show that any unsatisfiable set of linear inequalities has a cutting planes refutation in… (More)

- Nicola Galesi
- ITA
- 1997

Decision lists and decision trees are two models of computation for boolean functions. that rank-k decision trees are a subclass of decision lists. Here we identify precisely, by giving a syntactical characterization, the subclass of decision lists which correspond exactly to the class of bounded rank decision trees. Furthermore we give a more general… (More)

- Maria Luisa Bonet, Nicola Galesi
- Computational Complexity
- 2001

This paper is concerned with the complexity of proofs and of searching for proofs in resolution. We show that the recently proposed algorithm of Ben-Sasson & Wigderson for searching for proofs in resolution cannot give better than weakly exponential performance. This is a consequence of our main result: we show the optimality of the general relationship… (More)