127,801 research outputs found
Abstract Interpretation with Unfoldings
We present and evaluate a technique for computing path-sensitive interference
conditions during abstract interpretation of concurrent programs. In lieu of
fixed point computation, we use prime event structures to compactly represent
causal dependence and interference between sequences of transformers. Our main
contribution is an unfolding algorithm that uses a new notion of independence
to avoid redundant transformer application, thread-local fixed points to reduce
the size of the unfolding, and a novel cutoff criterion based on subsumption to
guarantee termination of the analysis. Our experiments show that the abstract
unfolding produces an order of magnitude fewer false alarms than a mature
abstract interpreter, while being several orders of magnitude faster than
solver-based tools that have the same precision.Comment: Extended version of the paper (with the same title and authors) to
appear at CAV 201
Kira - A Feynman Integral Reduction Program
In this article, we present a new implementation of the Laporta algorithm to
reduce scalar multi-loop integrals---appearing in quantum field theoretic
calculations---to a set of master integrals. We extend existing approaches by
using an additional algorithm based on modular arithmetic to remove linearly
dependent equations from the system of equations arising from
integration-by-parts and Lorentz identities. Furthermore, the algebraic
manipulations required in the back substitution are optimized. We describe in
detail the implementation as well as the usage of the program. In addition, we
show benchmarks for concrete examples and compare the performance to Reduze 2
and FIRE 5.
In our benchmarks we find that Kira is highly competitive with these existing
tools.Comment: 37 pages, 3 figure
Quantum resource estimates for computing elliptic curve discrete logarithms
We give precise quantum resource estimates for Shor's algorithm to compute
discrete logarithms on elliptic curves over prime fields. The estimates are
derived from a simulation of a Toffoli gate network for controlled elliptic
curve point addition, implemented within the framework of the quantum computing
software tool suite LIQ. We determine circuit implementations for
reversible modular arithmetic, including modular addition, multiplication and
inversion, as well as reversible elliptic curve point addition. We conclude
that elliptic curve discrete logarithms on an elliptic curve defined over an
-bit prime field can be computed on a quantum computer with at most qubits using a quantum circuit of at most Toffoli gates. We are able to classically simulate the
Toffoli networks corresponding to the controlled elliptic curve point addition
as the core piece of Shor's algorithm for the NIST standard curves P-192,
P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to
recent resource estimates for Shor's factoring algorithm. The results also
support estimates given earlier by Proos and Zalka and indicate that, for
current parameters at comparable classical security levels, the number of
qubits required to tackle elliptic curves is less than for attacking RSA,
suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added.
ASIACRYPT 201
Fast Quantum Modular Exponentiation
We present a detailed analysis of the impact on modular exponentiation of
architectural features and possible concurrent gate execution. Various
arithmetic algorithms are evaluated for execution time, potential concurrency,
and space tradeoffs. We find that, to exponentiate an n-bit number, for storage
space 100n (twenty times the minimum 5n), we can execute modular exponentiation
two hundred to seven hundred times faster than optimized versions of the basic
algorithms, depending on architecture, for n=128. Addition on a neighbor-only
architecture is limited to O(n) time when non-neighbor architectures can reach
O(log n), demonstrating that physical characteristics of a computing device
have an important impact on both real-world running time and asymptotic
behavior. Our results will help guide experimental implementations of quantum
algorithms and devices.Comment: to appear in PRA 71(5); RevTeX, 12 pages, 12 figures; v2 revision is
substantial, with new algorithmic variants, much shorter and clearer text,
and revised equation formattin
Fast Supervised Hashing with Decision Trees for High-Dimensional Data
Supervised hashing aims to map the original features to compact binary codes
that are able to preserve label based similarity in the Hamming space.
Non-linear hash functions have demonstrated the advantage over linear ones due
to their powerful generalization capability. In the literature, kernel
functions are typically used to achieve non-linearity in hashing, which achieve
encouraging retrieval performance at the price of slow evaluation and training
time. Here we propose to use boosted decision trees for achieving non-linearity
in hashing, which are fast to train and evaluate, hence more suitable for
hashing with high dimensional data. In our approach, we first propose
sub-modular formulations for the hashing binary code inference problem and an
efficient GraphCut based block search method for solving large-scale inference.
Then we learn hash functions by training boosted decision trees to fit the
binary codes. Experiments demonstrate that our proposed method significantly
outperforms most state-of-the-art methods in retrieval precision and training
time. Especially for high-dimensional data, our method is orders of magnitude
faster than many methods in terms of training time.Comment: Appearing in Proc. IEEE Conf. Computer Vision and Pattern
Recognition, 2014, Ohio, US
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