dag construction

To address the ambiguity and redundancy in DAG serialization arising from non-unique topological orders, this paper proposes a reversible generative framework based on an unambiguous context-free graph grammar: it uniquely maps each DAG to a deterministic sequence of production rules, eliminating reliance on topological sorting while ensuring representation compactness, uniqueness, and invertibility. Methodologically, we formulate DAG generation as an unambiguous syntactic derivation process—the first such formulation—and introduce a normalized traversal strategy coupled with a rule-serialization mechanism. The framework enables lossless DAG compression, differentiable graph generation, continuous latent-space learning for attribute prediction, and efficient Bayesian optimization over structured data. It combines theoretical rigor—guaranteeing bijective mapping—with interpretable, syntax-driven generation.

ROS 2’s publish-subscribe model lacks native support for enforcing priority and data-dependency constraints in directed acyclic graph (DAG)–structured tasks, resulting in out-of-order callback execution, inconsistent multi-input matching policies, and DAG semantics sustained solely through ad hoc programming conventions—rendering systems prone to instability and crashes. To address this, we propose the Function-as-Subtask (FasS) API: a declarative interface that explicitly models data flow via function parameters and return values, thereby enforcing DAG structure at the API level and eliminating reliance on developer discipline. We implement a native DAG-aware scheduler in Rust and design a system integration layer compatible with Linux’s sched_ext subsystem. Experimental evaluation demonstrates that FasS guarantees semantic fidelity while delivering a production-ready, real-time–capable DAG scheduling infrastructure.

This work proposes a novel architecture based on multi-scale context fusion and adaptive attention mechanisms to address the limited representational capacity of existing methods in complex scenes. By dynamically integrating local details with global semantic information, the proposed approach significantly enhances the model’s ability to capture fine-grained features. Extensive experiments demonstrate that the method achieves state-of-the-art performance across multiple benchmark datasets while maintaining superior inference efficiency compared to contemporary models. Beyond validating the effectiveness of context-adaptive modeling, this study also offers new insights into efficient visual understanding.

This work addresses the flow decomposition problem on general directed graphs (including cyclic ones), breaking the decade-long restriction to directed acyclic graphs (DAGs). We propose the first unifying framework based on dominator trees, pioneering their use for detecting safe edge sequences in cyclic graphs: we establish that the longest safe sequence corresponds to an expansion of common leaf nodes across two dominator trees and identify it in linear time. Integrated with mixed-integer linear programming (MILP), our framework leverages dominator-tree preprocessing to fix safe path variables a priori, drastically reducing model size and eliminating costly linearizations of nonlinear terms. Evaluated on four bacterial genome datasets, our approach achieves up to 1000× speedup; over 90% of instances are solved within 30 seconds. This significantly enhances both solvability and efficiency of minimum flow decomposition and minimum absolute error models.

This work addresses the challenge of reliably tracing the provenance of tensors and operators through graph rewrites—particularly non-injective transformations—in AI compilers. The authors propose a lightweight, generative provenance method grounded in observational semantics, which infers origins by analyzing the behavioral effects of graph transformations rather than relying on identifier propagation. For the first time, they introduce coalgebraic modeling and bisimulation to this domain, guaranteeing provenance consistency even after intermediate nodes are eliminated. The approach requires no invasive compiler modifications and naturally supports non-injective rewrites. Evaluated within COVAN, a prototype AI compiler, the method demonstrates stable, low-overhead provenance tracking throughout an end-to-end compilation pipeline.

Current prompt graphs lack a clear definition and standardized terminology, resulting in conceptual ambiguity in practice. This work addresses this gap by proposing a formal definition of prompt graph engineering through conceptual analysis, gray literature review, and systematic categorization. It identifies prompt graphs as first-class, executable, and improvable engineering artifacts and establishes four necessary constitutive conditions along with inclusion and exclusion criteria for operational validation. The proposed definition demonstrates consistent applicability across six major frameworks—including LangGraph and DSPy—thereby offering the field its first operational framework and shared vocabulary. Building on this foundation, the paper outlines a future research agenda structured around four key design tensions inherent to prompt graph development.

Existing Datalog engines struggle to simultaneously achieve efficiency, scalability, and extensible semantics in static analysis, while also lacking robust support for rule debugging and incremental updates. This work proposes a novel approach that compiles Soufflé-style Datalog programs into executable Differential Dataflow programs, yielding a high-performance, memory-efficient static analysis framework capable of millisecond-scale incremental recomputation. The framework natively supports non-standard semantics—such as k-core analysis—and integrates in-browser performance profiling and rule-tuning capabilities. Evaluated on 24 real-world static analysis benchmarks, the system outperforms state-of-the-art engines in both runtime performance and scalability.

This work addresses the challenges of contextual overhead and composability arising from the growing scale of tool libraries by proposing a framework that co-evolves planners and tool repositories. The approach constructs a code-native, composable directed acyclic graph (DAG), where each node represents a tool via its type signature, pre/post-conditions, natural language description, and usage examples. A typed DAG retrieval mechanism enables efficient reasoning by integrating symbolic unification, behavioral constraint filtering, and example-based disambiguation. Leveraging DAG-induced rewards and a conservative update strategy, the system enables an 8B-parameter model to match or even surpass the performance of a 32B teacher model on benchmarks such as GSM8K and MATH, significantly outperforming existing methods in tool utilization and skill acquisition.

This work addresses the challenge of identifying structural and semantic similarities across imperative programs written in different languages by proposing a unified graph representation that integrates abstract syntax trees with neural semantic embeddings. The approach transforms annotated programs into typed, attributed graphs and leverages CodeBERT and SentenceTransformer to generate rich semantic embeddings. By constructing consistent graph representations across multilingual verification datasets—including C/ACSL, Java/JML, and Dafny—it achieves, for the first time, joint modeling of syntactic structure and formal semantics. This unified framework offers a viable pathway for cross-language reuse of verification artifacts and demonstrates strong generality and effectiveness across diverse programming languages and specification frameworks.

This study addresses the problem of correctly and efficiently encoding compressed natural deduction proofs—represented as directed acyclic graphs, known as DLDSs—into Boolean circuits. Focusing on level-compressed DLDSs in pure implicational minimal logic, the work proposes a path-assignment-based dependency propagation semantics that guarantees logical equivalence between the original proof and its circuit encoding. Innovatively, it presents the first formalization in the Lean theorem prover of a verifiable mapping from DLDSs to Boolean circuits, and establishes a rigorous correspondence between path extraction in uncompressed tree-like fragments and circuit acceptance conditions. This contribution not only enables machine-verified translation but also provides a formally checkable circuit evaluator, thereby strengthening the foundation for certified proof-to-circuit transformations.