Bibliographic Information: Berkholz, C., Mengel, S., & Wilhelm, H. (2024). A characterization of efficiently compilable constraint languages. arXiv:2311.10040v2 [cs.LO].
Research Objective: This paper aims to identify the types of constraints, or constraint languages, that allow for the efficient computation of polynomial-sized representations in knowledge compilation, particularly focusing on DNNFs (Decomposable Negation Normal Forms) and decision diagrams.
Methodology: The researchers introduce the concepts of "strong blockwise decomposability" and "strong uniformly blockwise decomposability" as combinatorial properties of constraint languages. They develop polynomial-time algorithms for compiling constraint languages possessing these properties into DNNF, structured DNNF, FDD, and ODD representations. Conversely, for constraint languages lacking these properties, they construct families of CSP (Constraint Satisfaction Problem) instances requiring exponential-sized representations, thus proving the tightness of their characterization.
Key Findings: The study establishes a dichotomy for efficient knowledge compilation based on the properties of constraint languages:
Main Conclusions: The research provides a complete classification of efficiently compilable constraint languages for a range of knowledge compilation targets, ranging from ODDs to DNNFs. It demonstrates that the identified decomposability properties are both sufficient and necessary for efficient compilation.
Significance: This work significantly contributes to the field of knowledge compilation by providing a deep understanding of the relationship between constraint language complexity and the efficiency of compiling them into compact representations. This has implications for various areas where knowledge compilation is crucial, including constraint satisfaction, probabilistic inference, and database systems.
Limitations and Future Research: The paper primarily focuses on the theoretical characterization of efficiently compilable constraint languages. Future research could explore practical algorithms and heuristics for compiling these languages into different knowledge representation formats, potentially leading to more efficient solvers and reasoning systems. Additionally, investigating the applicability of these findings to other knowledge compilation targets beyond DNNFs and decision diagrams could be a fruitful avenue for future work.
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by Christoph Be... at arxiv.org 10-07-2024
https://arxiv.org/pdf/2311.10040.pdfDeeper Inquiries