Summary of Structured D-dnnf Is Not Closed Under Negation, by Harry Vinall-smeeth
Structured d-DNNF Is Not Closed Under Negation
by Harry Vinall-Smeeth
First submitted to arxiv on: 7 Feb 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: Logic in Computer Science (cs.LO)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper explores the complexity of OBDD, structured d-DNNF, and SDD in answering two open questions. Firstly, it investigates whether OBDD supports more tractable transformations than structured d-DNNF, concluding that OBDD is indeed more tractable due to polytime negation, disjunction, or existential quantification operations not being supported by structured d-DNNF. Secondly, the paper shows that there are functions with an equivalent polynomial-sized structured d-DNNF but no representation as an SDD, thus demonstrating a succinctness gap between PSDD and monotone AC analogue to structured d-DNNF. The results have significant implications for the study of OBDD, structured d-DNNF, and SDD. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about solving two big puzzles in a special area of computer science called Boolean reasoning. The researchers looked at three different ways to solve these problems: OBDD, structured d-DNNF, and SDD. They found that OBDD is better than the other two for certain tasks, but not as good when it comes to making calculations simpler. They also showed that some functions can be represented in one way (structured d-DNNF) but not another (SDD), which has important implications for how we think about these problems. |
