Cloud-Based Quadratic Optimization with Partially Homomorphic Encryption

This article develops a cloud-based protocol for a constrained quadratic optimization problem involving multiple parties, each holding private data. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure communication techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy. We show the implementation results of the protocol and discuss its computational and communication complexity. We conclude this article with a discussion on privacy notions

Towards Logical Specification of Statistical Machine Learning

We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification performance, robustness, and fairness of classifiers by using epistemic logic. Then we show some relationships among properties of classifiers and those between classification performance and robustness, which suggests robustness-related properties that have not been formalized in the literature as far as we know. To formalize fairness properties, we define a notion of counterfactual knowledge and show techniques to formalize conditional indistinguishability by using counterfactual epistemic operators. As far as we know, this is the first work that uses logical formulas to express statistical properties of machine learning, and that provides epistemic (resp. counterfactually epistemic) views on robustness (resp. fairness) of classifiers.Comment: SEFM'19 conference paper (full version with errors corrected

A weakness measure for GR(1) formulae

In spite of the theoretical and algorithmic developments for system synthesis in recent years, little effort has been dedicated to quantifying the quality of the specifications used for synthesis. When dealing with unrealizable specifications, finding the weakest environment assumptions that would ensure realizability is typically a desirable property; in such context the weakness of the assumptions is a major quality parameter. The question of whether one assumption is weaker than another is commonly interpreted using implication or, equivalently, language inclusion. However, this interpretation does not provide any further insight into the weakness of assumptions when implication does not hold. To our knowledge, the only measure that is capable of comparing two formulae in this case is entropy, but even it fails to provide a sufficiently refined notion of weakness in case of GR(1) formulae, a subset of linear temporal logic formulae which is of particular interest in controller synthesis. In this paper we propose a more refined measure of weakness based on the Hausdorff dimension, a concept that captures the notion of size of the omega-language satisfying a linear temporal logic formula. We identify the conditions under which this measure is guaranteed to distinguish between weaker and stronger GR(1) formulae. We evaluate our proposed weakness measure in the context of computing GR(1) assumptions refinements

Combining Induction, Deduction, and Structure for Verification and Synthesis

Even with impressive advances in formal methods, certain major challenges remain. Chief among these are environment modeling, incompleteness in specifications, and the hardness of underlying decision problems. In this paper, we characterize two trends that show great promise in meeting these challenges. The first trend is to perform verification by reduction to synthesis. The second is to solve the resulting synthesis problem by integrating traditional, deductive methods with inductive inference (learning from examples) using hypotheses about system structure. We present a formalization of such an integration, show how it can tackle hard problems in verification and synthesis, and outline directions for future work

Verifying high-confidence interactive systems: Electronic voting and beyond

Human interaction is central to many computing systems that require a high level of assurance. We term such systems as high-confidence interactive systems. Examples of such systems include aircraft control systems (interacting with a pilot), automobiles with self-driving features (interacting with a driver), medical devices (interacting with a doctor), and electronic voting machines (interacting with a voter). A major challenge to verifying the correct operation of such systems is that it is difficult to formally specify the human user's view of correct operation and perception of the input/output interface. In this paper, we describe a promising approach towards addressing this challenge that combines formal verification with systematic testing by humans. We describe an illustrative application of this approach to electronic voting in the U.S., and outline directions for future work. © Springer-Verlag 2013