9,364 research outputs found
SPEEDY: An Eclipse-based IDE for invariant inference
SPEEDY is an Eclipse-based IDE for exploring techniques that assist users in
generating correct specifications, particularly including invariant inference
algorithms and tools. It integrates with several back-end tools that propose
invariants and will incorporate published algorithms for inferring object and
loop invariants. Though the architecture is language-neutral, current SPEEDY
targets C programs. Building and using SPEEDY has confirmed earlier experience
demonstrating the importance of showing and editing specifications in the IDEs
that developers customarily use, automating as much of the production and
checking of specifications as possible, and showing counterexample information
directly in the source code editing environment. As in previous work,
automation of specification checking is provided by back-end SMT solvers.
However, reducing the effort demanded of software developers using formal
methods also requires a GUI design that guides users in writing, reviewing, and
correcting specifications and automates specification inference.Comment: In Proceedings F-IDE 2014, arXiv:1404.578
Algorithm Diversity for Resilient Systems
Diversity can significantly increase the resilience of systems, by reducing
the prevalence of shared vulnerabilities and making vulnerabilities harder to
exploit. Work on software diversity for security typically creates variants of
a program using low-level code transformations. This paper is the first to
study algorithm diversity for resilience. We first describe how a method based
on high-level invariants and systematic incrementalization can be used to
create algorithm variants. Executing multiple variants in parallel and
comparing their outputs provides greater resilience than executing one variant.
To prevent different parallel schedules from causing variants' behaviors to
diverge, we present a synchronized execution algorithm for DistAlgo, an
extension of Python for high-level, precise, executable specifications of
distributed algorithms. We propose static and dynamic metrics for measuring
diversity. An experimental evaluation of algorithm diversity combined with
implementation-level diversity for several sequential algorithms and
distributed algorithms shows the benefits of algorithm diversity
Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
A parameterization of the density operator, a coherence vector
representation, which uses a basis of orthogonal, traceless, Hermitian matrices
is discussed. Using this parameterization we find the region of permissible
vectors which represent a density operator. The inequalities which specify the
region are shown to involve the Casimir invariants of the group. In particular
cases, this allows the determination of degeneracies in the spectrum of the
operator. The identification of the Casimir invariants also provides a method
of constructing quantities which are invariant under {\it local} unitary
operations. Several examples are given which illustrate the constraints
provided by the positivity requirements and the utility of the coherence vector
parameterization.Comment: significantly rewritten and submitted for publicatio
Characterizing the geometrical edges of nonlocal two-qubit gates
Nonlocal two-qubit gates are geometrically represented by tetrahedron known
as Weyl chamber within which perfect entanglers form a polyhedron. We identify
that all edges of the Weyl chamber and polyhedron are formed by single
parametric gates. Nonlocal attributes of these edges are characterized using
entangling power and local invariants. In particular, SWAP (power)alpha family
of gates constitutes one edge of the Weyl chamber with SWAP-1/2 being the only
perfect entangler. Finally, optimal constructions of controlled-NOT using
SWAP-1/2 gate and gates belong to three edges of the polyhedron are presented.Comment: 11 pages, 4 figures, Phys. Rev. A 79, 052339 (2009
Entangling characterization of (SWAP)1/m and Controlled unitary gates
We study the entangling power and perfect entangler nature of (SWAP)1/m, for
m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only
perfect entangler in the family. On the other hand, a subset of CU which is
locally equivalent to CNOT is identified. It is shown that the subset, which is
a perfect entangler, must necessarily possess the maximum entangling power.Comment: 12 pages, 1 figure, One more paragraph added in Introductio
Monotones and invariants for multi-particle quantum states
We introduce new entanglement monotones which generalize, to the case of many
parties, those which give rise to the majorization-based partial ordering of
bipartite states' entanglement. We give some examples of restrictions they
impose on deterministic and probabilistic conversion between multipartite
states via local actions and classical communication. These include
restrictions which do not follow from any bipartite considerations. We derive
supermultiplicativity relations between each state's monotones and the
monotones for collective processing when the parties share several states. We
also investigate polynomial invariants under local unitary transformations, and
show that a large class of these are invariant under collective unitary
processing and also multiplicative, putting restrictions, for example, on the
exact conversion of multiple copies of one state to multiple copies of another.Comment: 25 pages, LaTe
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