确定性与非确定性传递闭包逻辑

[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science Pub Date : 1992-06-22 DOI:10.1109/LICS.1992.185519

E. Grädel, G. McColm

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引用次数: 10

摘要

证明了在无序结构上传递闭包逻辑(FO+TC)比确定性传递闭包逻辑(FO+DTC)严格地更强大。事实上，在某些图的类别上，例如大度和大周长的超立方体或正则图，(FO+DTC)中的每个查询都是一阶可表达的。另一方面，在这些类上有简单的(FO+pos TC)查询，不能用一阶公式定义。

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Deterministic vs. nondeterministic transitive closure logic

It is shown that transitive closure logic (FO+TC) is strictly more powerful than deterministic transitive closure logic (FO+DTC) on unordered structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every query in (FO+DTC) is first-order expressible. On the other hand, there are simple (FO+pos TC) queries on these classes that cannot be defined by first-order formulas.<>

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[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science

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