Neural Solving Uninterpreted Predicates with Abstract Gradient Descent

Uninterpreted predicate solving is a fundamental problem in formal verification, including loop invariant and constrained horn clauses predicate solving. Existing approaches have been mostly in symbolic ways. While achieving sustainable progress, they still suffer from inefficiency and seem unable to leverage the ever-increasing computility, such as GPU. Recently, neural relaxation has been proposed to tackle this problem. They treat the uninterpreted predicate-solving task as an optimization problem by relaxing the discrete search process into a learning process of neural networks. However, two bottlenecks keep them from being valid. First, relaxed neural networks cannot match the original semantics of predicates rigorously; second, the neural networks are difficult to train to reach global optimization. Therefore, this article presents a novel discrete neural architecture with the Abstract Gradient Decent (AGD) algorithm to directly solve uninterpreted predicates in the discrete hypothesis space. The abstract gradient is for discrete neurons whose calculation rules are designed in an abstract domain. Our approach conforms to the original semantics of predicates, and the proposed AGD algorithm can achieve global optimization satisfactorily. We implement the tool Dasp in the Boxes abstract domain to solve uninterpreted predicates in the QF-NIA SMT theory. In the experiments, Dasp has outperformed seven state-of-the-art tools across three predicate synthesis tasks.