1,440 research outputs found
Balancing Scalability and Uniformity in SAT Witness Generator
Constrained-random simulation is the predominant approach used in the
industry for functional verification of complex digital designs. The
effectiveness of this approach depends on two key factors: the quality of
constraints used to generate test vectors, and the randomness of solutions
generated from a given set of constraints. In this paper, we focus on the
second problem, and present an algorithm that significantly improves the
state-of-the-art of (almost-)uniform generation of solutions of large Boolean
constraints. Our algorithm provides strong theoretical guarantees on the
uniformity of generated solutions and scales to problems involving hundreds of
thousands of variables.Comment: This is a full version of DAC 2014 pape
Squeezing in driven bimodal Bose-Einstein Condensates: Erratic driving versus noise
We study the interplay of squeezing and phase randomization near the
hyperbolic instability of a two-site Bose-Hubbard model in the Josephson
interaction regime. We obtain results for the quantum Zeno suppression of
squeezing, far beyond the previously found short time behavior. More
importantly, we contrast the expected outcome with the case where randomization
is induced by erratic driving with the same fluctuations as the quantum noise
source, finding significant differences. These are related to the distribution
of the squeezing factor, which has log-normal characteristics: hence its
average is significantly different from its median due to the occurrence of
rare events.Comment: 5 pages, 4 figure
Distribution-Aware Sampling and Weighted Model Counting for SAT
Given a CNF formula and a weight for each assignment of values to variables,
two natural problems are weighted model counting and distribution-aware
sampling of satisfying assignments. Both problems have a wide variety of
important applications. Due to the inherent complexity of the exact versions of
the problems, interest has focused on solving them approximately. Prior work in
this area scaled only to small problems in practice, or failed to provide
strong theoretical guarantees, or employed a computationally-expensive maximum
a posteriori probability (MAP) oracle that assumes prior knowledge of a
factored representation of the weight distribution. We present a novel approach
that works with a black-box oracle for weights of assignments and requires only
an {\NP}-oracle (in practice, a SAT-solver) to solve both the counting and
sampling problems. Our approach works under mild assumptions on the
distribution of weights of satisfying assignments, provides strong theoretical
guarantees, and scales to problems involving several thousand variables. We
also show that the assumptions can be significantly relaxed while improving
computational efficiency if a factored representation of the weights is known.Comment: This is a full version of AAAI 2014 pape
The statistical strength of experiments to reject local realism with photon pairs and inefficient detectors
Because of the fundamental importance of Bell's theorem, a loophole-free
demonstration of a violation of local realism (LR) is highly desirable. Here,
we study violations of LR involving photon pairs. We quantify the experimental
evidence against LR by using measures of statistical strength related to the
Kullback-Leibler (KL) divergence, as suggested by van Dam et al. [W. van Dam,
R. Gill and P. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)].
Specifically, we analyze a test of LR with entangled states created from two
independent polarized photons passing through a polarizing beam splitter. We
numerically study the detection efficiency required to achieve a specified
statistical strength for the rejection of LR depending on whether photon
counters or detectors are used. Based on our results, we find that a test of LR
free of the detection loophole requires photon counters with efficiencies of at
least 89.71%, or photon detectors with efficiencies of at least 91.11%. For
comparison, we also perform this analysis with ideal unbalanced Bell states,
which are known to allow rejection of LR with detector efficiencies above 2/3.Comment: 18 pages, 3 figures, minor changes (add more references, replace the
old plots, etc.)
On Hashing-Based Approaches to Approximate DNF-Counting
Propositional model counting is a fundamental problem in artificial intelligence with a wide variety of applications, such as probabilistic inference, decision making under uncertainty, and
probabilistic databases. Consequently, the problem is of theoretical as well as practical interest. When the constraints are expressed as DNF formulas, Monte Carlo-based techniques have been shown to provide a fully polynomial randomized approximation scheme (FPRAS). For CNF constraints, hashing-based approximation techniques have been demonstrated to be highly successful. Furthermore, it was shown that hashing-based techniques also yield an FPRAS for DNF counting without usage of Monte Carlo sampling. Our analysis, however, shows that the proposed hashing-based approach to DNF counting provides poor time complexity compared to the Monte Carlo-based DNF counting techniques. Given the success of hashing-based techniques for CNF constraints, it is natural to ask: Can hashing-based techniques provide an efficient FPRAS for DNF counting? In this paper, we provide a positive answer to this question. To this end, we introduce two novel algorithmic techniques: Symbolic Hashing and Stochastic Cell Counting, along
with a new hash family of Row-Echelon hash functions. These innovations allow us to design a hashing-based FPRAS for DNF counting of similar complexity (up to polylog factors) as that
of prior works. Furthermore, we expect these techniques to have potential applications beyond DNF counting
Weak MSO+U with Path Quantifiers over Infinite Trees
This paper shows that over infinite trees, satisfiability is decidable for
weak monadic second-order logic extended by the unbounding quantifier U and
quantification over infinite paths. The proof is by reduction to emptiness for
a certain automaton model, while emptiness for the automaton model is decided
using profinite trees.Comment: version of an ICALP 2014 paper with appendice
Bose-enhanced chemistry: Amplification of selectivity in the dissociation of molecular Bose-Einstein condensates
We study the photodissociation chemistry of a quantum degenerate gas of
bosonic triatomic molecules, assuming two open rearrangement channels
( or ). The equations of motion are equivalent to those of a
parametric multimode laser, resulting in an exponential buildup of macroscopic
mode populations. By exponentially amplifying a small differential in the
single-particle rate-coefficients, Bose stimulation leads to a nearly complete
selectivity of the collective -body process, indicating a novel type of
ultra-selective quantum degenerate chemistry.Comment: 5 pages, 3 figure
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