Browsing by Author "Galesi, Nicola"
Now showing items 1-8 of 8
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A Syntactic characterization of bounded-rank decision trees in terms of decision lsts
(1996-03-06)
Research report
Open AccessDecision lists and decision trees are two models of computation for boolean functions. Blum has shown (Information Processing Letters 42 (1992), 183-185) that rank-k decision trees are a subclass of decision lists. ... -
Exponential separation between tree-like and dag-like Cutting Planes proof systems
(1997-12)
Research report
Open AccessWe prove an exponential lower bound for tree-like Cutting Planes refutations of a set of clauses which has polynomial size resolution refutations. This implies an exponential separation between tree-like and dag-like ... -
Linear lower bounds and simulations in Frege systems with substitutions
(1996-10)
Research report
Open AccessOur work concerns Frege systems, substitution Frege systems (sF), renaming Frege systems, top/bottom-Frege systems and extended Frege systems (eF). Urquhart shows that tautologies associated to a binary strings ... -
Monotone proofs of the pigeon hole principle
(2000-04)
Research report
Open AccessWe 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 ... -
On the complexity of resolution with bounded conjunctions
(2003-06)
Research report
Open AccessWe analyze size and space complexity of Res(k), a family of propositional proof systems introduced by Kraj which extend Resolution by allowing disjunctions of conjunctions of up to 1$ literals. We show that the ... -
On vanishing sums of roots of unity in polynomial calculus and sum-of-squares
(2023-12)
Article
Open AccessWe introduce a novel take on sum-of-squares that is able to reason with complex numbers and still make use of polynomial inequalities. This proof system might be of independent interest since it allows to represent multivalued ... -
On vanishing sums of roots of unity in polynomial calculus and sum-of-squares
(Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022)
Conference report
Open AccessVanishing sums of roots of unity can be seen as a natural generalization of knapsack from Boolean variables to variables taking values over the roots of unity. We show that these sums are hard to prove for polynomial ... -
The Width-size method for general resolution is optimal
(1999-02)
Research report
Open AccessThe Width-Size Method for resolution was recently introduced by Ben-Sasson and Wigderson (BSW): Short Proofs are Narrow - Resolution Made Simple STOC 99). They found a trade-off between two complexity measures for ...
