SMT(LIA) Sampling with High Diversity

2025-02-25

arXiv.org

AI Summary

Existing SMT sampling methods for Linear Integer Arithmetic (LIA) constraints suffer from insufficient solution diversity and low efficiency, failing to meet practical demands for diverse test inputs. This paper proposes HighDiv, the first SMT(LIA) diverse solution generation framework integrating local search with randomized CDCL(T). Its key contributions are: (1) a boundary-aware move operator that enhances local search exploration near constraint boundaries; (2) deep optimization of preprocessing and variable initialization strategies; and (3) the first approach to guide CDCL(T) jumps into novel solution subspaces using local search solutions as constraints. Experimental evaluation demonstrates that HighDiv significantly outperforms the state-of-the-art tool MeGASampler in diversity metrics, thereby improving both coverage breadth and effectiveness of generated test inputs.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Satisfiability Modulo Linear Integer Arithmetic, SMT(LIA) for short, is pivotal across various critical domains. Previous research has primarily focused on SMT solving techniques. However, in practical applications such as software and hardware testing, there is a need to generate a diverse set of solutions for use as test inputs. We have developed the first sampling framework that integrates local search with CDCL(T) techniques, named HighDiv, capable of generating a highly diverse set of solutions for constraints under linear integer theory. Initially, in the local search phase, we introduced a novel operator called boundary-aware movement. This operator performs random moves by considering the current state's constraints on variables, thereby enhancing the diversity of variables during the search process. Furthermore, we have conducted an in-depth study of the preprocessing and variable initialization mechanisms within the framework, which significantly enhances the efficiency of subsequent local searches. Lastly, we use the solutions obtained from local search sampling as additional constraints to further explore the solution space using the stochastic CDCL(T) method. Experimental results demonstrate that HighDiv generates solutions with greater diversity compared to the state-of-the-art SMT(LIA) sampling tool, MeGASampler.

Problem

• Generating diverse solutions for SMT(LIA) constraints
• Integrating local search with CDCL(T) sampling techniques
• Enhancing solution diversity for software/hardware testing inputs

Innovation

• Integrates local search with CDCL(T) techniques
• Introduces boundary-aware movement operator
• Uses local solutions as constraints for CDCL(T)