12,207 research outputs found
Efficient Interpolation for the Theory of Arrays
Existing techniques for Craig interpolation for the quantifier-free fragment
of the theory of arrays are inefficient for computing sequence and tree
interpolants: the solver needs to run for every partitioning of the
interpolation problem to avoid creating -mixed terms. We present a new
approach using Proof Tree Preserving Interpolation and an array solver based on
Weak Equivalence on Arrays. We give an interpolation algorithm for the lemmas
produced by the array solver. The computed interpolants have worst-case
exponential size for extensionality lemmas and worst-case quadratic size
otherwise. We show that these bounds are strict in the sense that there are
lemmas with no smaller interpolants. We implemented the algorithm and show that
the produced interpolants are useful to prove memory safety for C programs.Comment: long version of the paper at IJCAR 201
Privacy-Preserving Secret Shared Computations using MapReduce
Data outsourcing allows data owners to keep their data at \emph{untrusted}
clouds that do not ensure the privacy of data and/or computations. One useful
framework for fault-tolerant data processing in a distributed fashion is
MapReduce, which was developed for \emph{trusted} private clouds. This paper
presents algorithms for data outsourcing based on Shamir's secret-sharing
scheme and for executing privacy-preserving SQL queries such as count,
selection including range selection, projection, and join while using MapReduce
as an underlying programming model. Our proposed algorithms prevent an
adversary from knowing the database or the query while also preventing
output-size and access-pattern attacks. Interestingly, our algorithms do not
involve the database owner, which only creates and distributes secret-shares
once, in answering any query, and hence, the database owner also cannot learn
the query. Logically and experimentally, we evaluate the efficiency of the
algorithms on the following parameters: (\textit{i}) the number of
communication rounds (between a user and a server), (\textit{ii}) the total
amount of bit flow (between a user and a server), and (\textit{iii}) the
computational load at the user and the server.\BComment: IEEE Transactions on Dependable and Secure Computing, Accepted 01
Aug. 201
Analyticity of The Ground State Energy For Massless Nelson Models
We show that the ground state energy of the translationally invariant Nelson
model, describing a particle coupled to a relativistic field of massless
bosons, is an analytic function of the coupling constant and the total
momentum. We derive an explicit expression for the ground state energy which is
used to determine the effective mass.Comment: 33 pages, 1 figure, added a section on the calculation of the
effective mas
Cut-elimination for the modal Grzegorczyk logic via non-well-founded proofs
We present a sequent calculus for the modal Grzegorczyk logic Grz allowing
non-well-founded proofs and obtain the cut-elimination theorem for it by
constructing a continuous cut-elimination mapping acting on these proofs.Comment: WOLLIC'17, 12 pages, 1 appendi
Gromov-Monge quasi-metrics and distance distributions
Applications in data science, shape analysis and object classification
frequently require maps between metric spaces which preserve geometry as
faithfully as possible. In this paper, we combine the Monge formulation of
optimal transport with the Gromov-Hausdorff distance construction to define a
measure of the minimum amount of geometric distortion required to map one
metric measure space onto another. We show that the resulting quantity, called
Gromov-Monge distance, defines an extended quasi-metric on the space of
isomorphism classes of metric measure spaces and that it can be promoted to a
true metric on certain subclasses of mm-spaces. We also give precise
comparisons between Gromov-Monge distance and several other metrics which have
appeared previously, such as the Gromov-Wasserstein metric and the continuous
Procrustes metric of Lipman, Al-Aifari and Daubechies. Finally, we derive
polynomial-time computable lower bounds for Gromov-Monge distance. These lower
bounds are expressed in terms of distance distributions, which are classical
invariants of metric measure spaces summarizing the volume growth of metric
balls. In the second half of the paper, which may be of independent interest,
we study the discriminative power of these lower bounds for simple subclasses
of metric measure spaces. We first consider the case of planar curves, where we
give a counterexample to the Curve Histogram Conjecture of Brinkman and Olver.
Our results on plane curves are then generalized to higher dimensional
manifolds, where we prove some sphere characterization theorems for the
distance distribution invariant. Finally, we consider several inverse problems
on recovering a metric graph from a collection of localized versions of
distance distributions. Results are derived by establishing connections with
concepts from the fields of computational geometry and topological data
analysis.Comment: Version 2: Added many new results and improved expositio
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