Towards Realizability Checking of Contracts using Theories

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. Such proofs build from "leaf-level" assume/guarantee component contracts through architectural layers towards top-level safety properties. The proofs are built upon the premise that each leaf-level component contract is realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. Without engineering support it is all too easy to write leaf-level components that can't be realized. Realizability checking for propositional contracts has been well-studied for many years, both for component synthesis and checking correctness of temporal logic requirements. However, checking realizability for contracts involving infinite theories is still an open problem. In this paper, we describe a new approach for checking realizability of contracts involving theories and demonstrate its usefulness on several examples.Comment: 15 pages, to appear in NASA Formal Methods (NFM) 201

Beating the Perils of Non-Convexity: Guaranteed Training of Neural Networks using Tensor Methods

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of two-layer neural networks. We provide risk bounds for our proposed method, with a polynomial sample complexity in the relevant parameters, such as input dimension and number of neurons. While learning arbitrary target functions is NP-hard, we provide transparent conditions on the function and the input for learnability. Our training method is based on tensor decomposition, which provably converges to the global optimum, under a set of mild non-degeneracy conditions. It consists of simple embarrassingly parallel linear and multi-linear operations, and is competitive with standard stochastic gradient descent (SGD), in terms of computational complexity. Thus, we propose a computationally efficient method with guaranteed risk bounds for training neural networks with one hidden layer.Comment: The tensor decomposition analysis is expanded, and the analysis of ridge regression is added for recovering the parameters of last layer of neural networ

Parameterized Synthesis

We study the synthesis problem for distributed architectures with a parametric number of finite-state components. Parameterized specifications arise naturally in a synthesis setting, but thus far it was unclear how to detect realizability and how to perform synthesis in a parameterized setting. Using a classical result from verification, we show that for a class of specifications in indexed LTL\X, parameterized synthesis in token ring networks is equivalent to distributed synthesis in a network consisting of a few copies of a single process. Adapting a well-known result from distributed synthesis, we show that the latter problem is undecidable. We describe a semi-decision procedure for the parameterized synthesis problem in token rings, based on bounded synthesis. We extend the approach to parameterized synthesis in token-passing networks with arbitrary topologies, and show applicability on a simple case study. Finally, we sketch a general framework for parameterized synthesis based on cutoffs and other parameterized verification techniques.Comment: Extended version of TACAS 2012 paper, 29 page

How to find real-world applications for compressive sensing

The potential of compressive sensing (CS) has spurred great interest in the research community and is a fast growing area of research. However, research translating CS theory into practical hardware and demonstrating clear and significant benefits with this hardware over current, conventional imaging techniques has been limited. This article helps researchers to find those niche applications where the CS approach provides substantial gain over conventional approaches by articulating lessons learned in finding one such application; sea skimming missile detection. As a proof of concept, it is demonstrated that a simplified CS missile detection architecture and algorithm provides comparable results to the conventional imaging approach but using a smaller FPA. The primary message is that all of the excitement surrounding CS is necessary and appropriate for encouraging our creativity but we all must also take off our "rose colored glasses" and critically judge our ideas, methods and results relative to conventional imaging approaches.Comment: 10 page

Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page