4,092 research outputs found
Polylogarithmic Cuts in Models of V^0
We study initial cuts of models of weak two-sorted Bounded Arithmetics with
respect to the strength of their theories and show that these theories are
stronger than the original one. More explicitly we will see that
polylogarithmic cuts of models of are models of
by formalizing a proof of Nepomnjascij's Theorem in such cuts. This is a
strengthening of a result by Paris and Wilkie. We can then exploit our result
in Proof Complexity to observe that Frege proof systems can be sub
exponentially simulated by bounded depth Frege proof systems. This result has
recently been obtained by Filmus, Pitassi and Santhanam in a direct proof. As
an interesting observation we also obtain an average case separation of
Resolution from AC0-Frege by applying a recent result with Tzameret.Comment: 16 page
Compression bounds for Lipschitz maps from the Heisenberg group to
We prove a quantitative bi-Lipschitz nonembedding theorem for the Heisenberg
group with its Carnot-Carath\'eodory metric and apply it to give a lower bound
on the integrality gap of the Goemans-Linial semidefinite relaxation of the
Sparsest Cut problem
Communication Complexity of Cake Cutting
We study classic cake-cutting problems, but in discrete models rather than
using infinite-precision real values, specifically, focusing on their
communication complexity. Using general discrete simulations of classical
infinite-precision protocols (Robertson-Webb and moving-knife), we roughly
partition the various fair-allocation problems into 3 classes: "easy" (constant
number of rounds of logarithmic many bits), "medium" (poly-logarithmic total
communication), and "hard". Our main technical result concerns two of the
"medium" problems (perfect allocation for 2 players and equitable allocation
for any number of players) which we prove are not in the "easy" class. Our main
open problem is to separate the "hard" from the "medium" classes.Comment: Added efficient communication protocol for the monotone crossing
proble
Kripke Models for Classical Logic
We introduce a notion of Kripke model for classical logic for which we
constructively prove soundness and cut-free completeness. We discuss the
novelty of the notion and its potential applications
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