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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)

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)

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)

We study the complexity of proving the Pigeon Hole Principle (PHP) in a monotone variant of the Gentzen Calculus, also known as Geometric Logic. We show that the standard encoding of the PHP as a monotone sequent admits quasipolynomial-size proofs in this system. This result is a consequence of deriving the basic properties of certain quasipolynomial-size… (More)

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)

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)

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

We deene syntactically a sub-class of decision lists (tree-like decision lists) and we show its equivalence with the class of bounded rank decision trees. As a by-product, the main theorem provides an alternate and easier proof of the Blum's containement Theorem 1]. Furthermore we give an inversion procedure for Blum's derivation of a decision list from a… (More)

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)