Abstract. In dynamic languages, objects are open-they support iteration over and dynamic addition/deletion of their attributes. Open objects, because they have an unbounded number of attributes, are difficult to abstract without a priori knowledge of all or nearly all of the attributes and thus pose a significant challenge for precise static analysis. To address this challenge, we present the HOO (Heap with Open Objects) abstraction that can precisely represent and infer properties about open-objectmanipulating programs without any knowledge of specific attributes. It achieves this by building upon a relational abstract domain for sets that is used to reason about partitions of object attributes. An implementation of the resulting static analysis is used to verify specifications for dynamic language framework code that makes extensive use of open objects, thus demonstrating the effectiveness of this approach.

Abstract. Digital filters are simple yet ubiquitous components of a wide variety of digital processing and control systems. Errors in the filters can be catastrophic. Traditionally digital filters have been verified using methods from control theory and extensive testing. We study two alternative verification techniques: bitprecise analysis and real-valued error approximations. In this paper, we empirically evaluate several variants of these two fundamental approaches for verifying fixed-point implementations of digital filters. We design our comparison to reveal the best possible approach towards verifying real-world designs of infinite impulse response (IIR) digital filters. Our study reveals broader insights into cases where bit-reasoning is absolutely necessary and suggests efficient approaches using modern satisfiability-modulo-theories (SMT) solvers.

Abstract. Programs written in modern languages perform intricate manipulations of containers such as arrays, lists, dictionaries, and sets. We present an abstract interpretation-based framework for automatically inferring relations between the set of values stored in these containers. Relations include inclusion relations over unions and intersections, as well as quantified relationships with scalar variables. We develop an abstract domain constructor that builds a container domain out of a Quantified Union-Intersection Constraint (QUIC) graph parameterized by an arbitrary base domain. We instantiate our domain with a polyhedral base domain and evaluate it on programs extracted from the Python test suite. Over traditional, non-relational domains, we find significant precision improvements with minimal performance cost.