Synthesizing Best Abstract Transformers via Parallel Bit-Vector Optimization

2026-06-15

AI Summary

This work addresses the challenge of efficiently synthesizing precision-optimal abstract transformers for low-level code represented using fixed-length bit-vectors. The authors propose Spear, a novel framework that, for the first time, formulates this task as a parallelizable multi-objective optimization problem. By exploiting independence among bit-vector objectives, Spear overcomes the scalability limitations of existing approaches. The framework integrates Optimization Modulo Theories (OMT), bit-vector abstract interpretation, and a parallel synthesis mechanism. Evaluated on two binary analysis benchmarks, Spear substantially outperforms state-of-the-art OMT solvers, solving more instances while achieving significantly reduced runtimes.

Abstract

Abstract interpretation provides a principled foundation for constructing sound static analyses through systematic abstraction. A central challenge is synthesizing the best abstract transformers that achieve optimal precision within a given abstract domain. This paper addresses this problem for low-level code modeled with fixed-size bit-vectors. Recent approaches formulate the synthesis task as a multi-objective Optimization Modulo Theories (OMT) problem, but suffer from limited scalability. We introduce Spear, a parallel synthesis framework that exploits a key structural insight: while the bits within each objective must be processed sequentially, the objectives themselves are independent. Spear leverages the independence of inter-objective bits to better parallelize the synthesis. Experimental results on benchmarks across two binary analysis domains show that Spear consistently outperforms state-of-the-art OMT solvers, solving more instances and achieving significantly improved runtimes. To our knowledge, this is the first approach to apply parallelism to accelerate the synthesis of optimal abstract transformers.

Problem

• abstract transformers
• bit-vector
• synthesis
• static analysis
• optimization

Innovation

• parallel synthesis
• abstract transformers
• bit-vector optimization
• Optimization Modulo Theories
• static analysis