We introduce Stencil-Lifting, a novel system for automatically converting stencil kernels written in low-level languages within legacy code into semantically equivalent Domain-Specific Language (DSL) implementations. Targeting the efficiency bottlenecks of existing verified lifting systems, Stencil-Lifting achieves scalable stencil kernel abstraction through two key innovations. First, we propose a hierarchical recursive lifting theory that represents stencil kernels, structured as nested loops, using invariant subgraphs, which are customized data dependency graphs capturing loop-carried computations and structural invariants. Each vertex in the invariant subgraph is associated with a predicate-based summary that encodes its computational semantics. Enforcing self-consistency across these summaries enables a derivation of correct loop invariants and postconditions, without the need for external verification. Second, we design a hierarchical recursive lifting algorithm that guarantees termination through a convergent recursive process, avoiding the inefficiencies of search-based synthesis while efficiently deriving valid summaries with formally proven completeness. We evaluate Stencil-Lifting on diverse stencil benchmarks from real-world applications. Experiment results demonstrate that Stencil-Lifting achieves 31.6× and 5.8× speedups compared to the state-of-the-art verified lifting systems STNG and Dexter, respectively. Our work significantly improves the efficiency of translating stencil kernels into DSL implementations, effectively bridging the gap between legacy code and modern DSL-based paradigms.

BACKGROUND: Brain image genetics provides enormous opportunities for examining the effects of genetic variations on the brain. Many studies have shown that the structure, function, and abnormality (e.g., those related to Alzheimer's disease) of the brain are heritable. However, which genetic variations contribute to these phenotypic changes is not completely clear. Advances in neuroimaging and genetics have led us to obtain detailed brain anatomy and genome-wide information. These data offer us new opportunities to identify genetic variations such as single nucleotide polymorphisms (SNPs) that affect brain structure. In this paper, we perform a genome-wide variant-based study, and aim to identify top SNPs or SNP sets which have genetic effects with the largest neuroanotomic coverage at both voxel and region-of-interest (ROI) levels. Based on the voxelwise genome-wide association study (GWAS) results, we used the exhaustive search to find the top SNPs or SNP sets that have the largest voxel-based or ROI-based neuroanatomic coverage. For SNP sets with >2 SNPs, we proposed an efficient genetic algorithm to identify top SNP sets that can cover all ROIs or a specific ROI. RESULTS: We identified an ensemble of top SNPs, SNP-pairs and SNP-sets, whose effects have the largest neuroanatomic coverage. Experimental results on real imaging genetics data show that the proposed genetic algorithm is superior to the exhaustive search in terms of computational time for identifying top SNP-sets. CONCLUSIONS: We proposed and applied an informatics strategy to identify top SNPs, SNP-pairs and SNP-sets that have genetic effects with the largest neuroanatomic coverage. The proposed genetic algorithm offers an efficient solution to accomplish the task, especially for identifying top SNP-sets.