RPP: Automatic Proof of Relational Properties by Self-Composition

Self-composition provides a powerful theoretical approach to prove relational properties, i.e. properties relating several program executions, that has been applied to compare two runs of one or similar programs (in secure dataflow properties, code transformations, etc.). This tool demo paper presents RPP, an original implementation of self-composition for specification and verification of relational properties in C programs in the FRAMA-C platform. We consider a very general notion of relational properties invoking any finite number of function calls of possibly dissimilar functions with possible nested calls. The new tool allows the user to specify a relational property, to prove it in a completely automatic way using classic deductive verification, and to use it as a hypothesis in the proof of other properties that may rely on it

Specifying and Testing kk-Safety Properties for Machine-Learning Models

Machine-learning models are becoming increasingly prevalent in our lives, for instance assisting in image-classification or decision-making tasks. Consequently, the reliability of these models is of critical importance and has resulted in the development of numerous approaches for validating and verifying their robustness and fairness. However, beyond such specific properties, it is challenging to specify, let alone check, general functional-correctness expectations from models. In this paper, we take inspiration from specifications used in formal methods, expressing functional-correctness properties by reasoning about $k$ different executions, so-called $k$-safety properties. Considering a credit-screening model of a bank, the expected property that "if a person is denied a loan and their income decreases, they should still be denied the loan" is a 2-safety property. Here, we show the wide applicability of $k$-safety properties for machine-learning models and present the first specification language for expressing them. We also operationalize the language in a framework for automatically validating such properties using metamorphic testing. Our experiments show that our framework is effective in identifying property violations, and that detected bugs could be used to train better models

Relational Logic with Framing and Hypotheses

Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs of intermediate steps, has been used in numerous guises, but existing relational program logics are narrow in scope. This paper introduces a logic based on novel syntax that weaves together product programs to express alignment of control flow points at which relational formulas are asserted. Correctness judgments feature hypotheses with relational specifications, discharged by a rule for the linking of procedure implementations. The logic supports reasoning about program-pairs containing both similar and dissimilar control and data structures. Reasoning about dynamically allocated objects is supported by a frame rule based on frame conditions amenable to SMT provers. We prove soundness and sketch how the logic can be used for data abstraction, loop optimizations, and secure information flow

Relational Symbolic Execution

Symbolic execution is a classical program analysis technique used to show that programs satisfy or violate given specifications. In this work we generalize symbolic execution to support program analysis for relational specifications in the form of relational properties - these are properties about two runs of two programs on related inputs, or about two executions of a single program on related inputs. Relational properties are useful to formalize notions in security and privacy, and to reason about program optimizations. We design a relational symbolic execution engine, named RelSym which supports interactive refutation, as well as proving of relational properties for programs written in a language with arrays and for-like loops