MSO-枚举 over SLP-压缩的无排名森林
MSO-Enumeration Over SLP-Compressed Unranked Forests
AI总结：
研究如何在SLP压缩的无排名森林上用单模第二阶逻辑枚举查询答案，提出线性预处理和输出线性延迟算法，扩展了树和字符串的MSO逻辑枚举结果。
摘要：
我们研究了在由直线路程程序（SLP）压缩的无排名森林F上，用单模第二阶逻辑（MSO）公式查询答案的枚举问题。我们的主要结果表明，可以在O(|D|)预处理后，以输出线性延迟（在数据复杂度下）完成枚举。这比之前已知的树上MSO评估算法有显著改进，因为|D|可能远小于或甚至与|F|的对数成正比，且存在线性时间SLP压缩器，可对实际输入提供良好的压缩。特别是，这构成了算法学中SLP压缩输入领域的一个元定理：所有可由MSO逻辑公式表达的树或字符串上的枚举问题，均可在线性预处理和输出线性延迟下解决，即使输入被SLP压缩。我们还展示了我们的方法可以支持顶点重标记更新，其时间复杂度与未压缩数据成对数关系。我们的结果扩展了之前关于未压缩树上MSO查询枚举以及压缩文本文档上文档跨度器枚举的工作。
英文摘要：
We study the problem of enumerating the answers to a query formulated in monadic second order logic (MSO) over an unranked forest F that is compressed by a straight-line program (SLP) D. Our main result states that this can be done after O(|D|) preprocessing and with output-linear delay (in data complexity). This is a substantial improvement over the previously known algorithms for MSO-evaluation over trees, since the compressed size |D| might be much smaller than (or even logarithmic in) the actual data size |F|, and there are linear time SLP-compressors that yield very good compressions on practical inputs. In particular, this also constitutes a meta-theorem in the field of algorithmics on SLP-compressed inputs: all enumeration problems on trees or strings that can be formulated in MSO-logic can be solved with linear preprocessing and output-linear delay, even if the inputs are compressed by SLPs. We also show that our approach can support vertex relabelling updates in time that is logarithmic in the uncompressed data. Our result extends previous work on the enumeration of MSO-queries over uncompressed trees and on the enumeration of document spanners over compressed text documents.
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