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