9,159 research outputs found
Bounded Quantifier Instantiation for Checking Inductive Invariants
We consider the problem of checking whether a proposed invariant
expressed in first-order logic with quantifier alternation is inductive, i.e.
preserved by a piece of code. While the problem is undecidable, modern SMT
solvers can sometimes solve it automatically. However, they employ powerful
quantifier instantiation methods that may diverge, especially when is
not preserved. A notable difficulty arises due to counterexamples of infinite
size.
This paper studies Bounded-Horizon instantiation, a natural method for
guaranteeing the termination of SMT solvers. The method bounds the depth of
terms used in the quantifier instantiation process. We show that this method is
surprisingly powerful for checking quantified invariants in uninterpreted
domains. Furthermore, by producing partial models it can help the user diagnose
the case when is not inductive, especially when the underlying reason
is the existence of infinite counterexamples.
Our main technical result is that Bounded-Horizon is at least as powerful as
instrumentation, which is a manual method to guarantee convergence of the
solver by modifying the program so that it admits a purely universal invariant.
We show that with a bound of 1 we can simulate a natural class of
instrumentations, without the need to modify the code and in a fully automatic
way. We also report on a prototype implementation on top of Z3, which we used
to verify several examples by Bounded-Horizon of bound 1
Quantum matchgate computations and linear threshold gates
The theory of matchgates is of interest in various areas in physics and
computer science. Matchgates occur in e.g. the study of fermions and spin
chains, in the theory of holographic algorithms and in several recent works in
quantum computation. In this paper we completely characterize the class of
boolean functions computable by unitary two-qubit matchgate circuits with some
probability of success. We show that this class precisely coincides with that
of the linear threshold gates. The latter is a fundamental family which appears
in several fields, such as the study of neural networks. Using the above
characterization, we further show that the power of matchgate circuits is
surprisingly trivial in those cases where the computation is to succeed with
high probability. In particular, the only functions that are
matchgate-computable with success probability greater than 3/4 are functions
depending on only a single bit of the input
Quadratic Scaling Bosonic Path Integral Molecular Dynamics
We present an algorithm for bosonic path integral molecular dynamics
simulations, which reduces the computational complexity with the number of
particles from cubic to quadratic. Path integral molecular dynamics simulations
of large bosonic systems are challenging, since a straightforward
implementation scales exponentially with the number of particles. We recently
developed a recursive algorithm that reduced the computational complexity from
exponential to cubic. It allowed performing the first path integral molecular
dynamics simulations of ~100 bosons, but the cubic scaling hindered
applications to much larger systems. Here, we report an improved algorithm that
scales only quadratically with system size. Simulations with our new method are
orders of magnitude faster, with a speedup that scales as , where and
are the number of beads (imaginary time slices) and particles,
respectively. In practice, this eliminates most of the cost of including
bosonic exchange effects in path integral molecular dynamics simulations. We
use the algorithm to simulate thousands of interacting bosons using path
integral molecular dynamics for the first time, spending days of computation on
simulations that would have otherwise taken decades to complete
Interplay between structure and magnetism in nanowires
We investigate the equilibrium geometry and electronic structure of
MoSI nanowires using ab initio Density Functional
calculations. The skeleton of these unusually stable nanowires consists of
rigid, functionalized Mo octahedra, connected by flexible, bi-stable sulphur
bridges. This structural flexibility translates into a capability to stretch up
to approximate 20% at almost no energy cost. The nanowires change from
conductors to narrow-gap magnetic semiconductors in one of their structural
isomers.Comment: 4 pages with PRL standards and 3 figure
Electrical Manipulation of Nanomagnets
We demonstrate a possibility to manipulate the magnetic coupling between two
nanomagnets with a help of ac electric field. In the scheme suggested the
magnetic coupling in question is mediated by a magnetic particle contacting
with both of the nanomagnets through the tunnel barriers. The electric field
providing a successive suppression of the barriers leads to pumping of
magnetization through the mediating particle. Time dependent dynamics of the
particle magnetization allows to to switch between ferro- and antiferromagnetic
couplings.Comment: 4 pages, 2 figure
Computing Stable Coalitions: Approximation Algorithms for Reward Sharing
Consider a setting where selfish agents are to be assigned to coalitions or
projects from a fixed set P. Each project k is characterized by a valuation
function; v_k(S) is the value generated by a set S of agents working on project
k. We study the following classic problem in this setting: "how should the
agents divide the value that they collectively create?". One traditional
approach in cooperative game theory is to study core stability with the
implicit assumption that there are infinite copies of one project, and agents
can partition themselves into any number of coalitions. In contrast, we
consider a model with a finite number of non-identical projects; this makes
computing both high-welfare solutions and core payments highly non-trivial.
The main contribution of this paper is a black-box mechanism that reduces the
problem of computing a near-optimal core stable solution to the purely
algorithmic problem of welfare maximization; we apply this to compute an
approximately core stable solution that extracts one-fourth of the optimal
social welfare for the class of subadditive valuations. We also show much
stronger results for several popular sub-classes: anonymous, fractionally
subadditive, and submodular valuations, as well as provide new approximation
algorithms for welfare maximization with anonymous functions. Finally, we
establish a connection between our setting and the well-studied simultaneous
auctions with item bidding; we adapt our results to compute approximate pure
Nash equilibria for these auctions.Comment: Under Revie
R-parity Conservation via the Stueckelberg Mechanism: LHC and Dark Matter Signals
We investigate the connection between the conservation of R-parity in
supersymmetry and the Stueckelberg mechanism for the mass generation of the B-L
vector gauge boson. It is shown that with universal boundary conditions for
soft terms of sfermions in each family at the high scale and with the
Stueckelberg mechanism for generating mass for the B-L gauge boson present in
the theory, electric charge conservation guarantees the conservation of
R-parity in the minimal B-L extended supersymmetric standard model. We also
discuss non-minimal extensions. This includes extensions where the gauge
symmetries arise with an additional U(1)_{B-L} x U(1)_X, where U(1)_X is a
hidden sector gauge group. In this case the presence of the additional U(1)_X
allows for a Z' gauge boson mass with B-L interactions to lie in the sub-TeV
region overcoming the multi-TeV LEP constraints. The possible tests of the
models at colliders and in dark matter experiments are analyzed including
signals of a low mass Z' resonance and the production of spin zero bosons and
their decays into two photons. In this model two types of dark matter
candidates emerge which are Majorana and Dirac particles. Predictions are made
for a possible simultaneous observation of new physics events in dark matter
experiments and at the LHC.Comment: 38 pages, 7 fig
Optimal Principal Component Analysis in Distributed and Streaming Models
We study the Principal Component Analysis (PCA) problem in the distributed
and streaming models of computation. Given a matrix a
rank parameter , and an accuracy parameter , we
want to output an orthonormal matrix for which where is the best rank- approximation to .
This paper provides improved algorithms for distributed PCA and streaming
PCA.Comment: STOC2016 full versio
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