关于用简洁图表示的单称二阶公式难度
Hardness of monadic second-order formulae over succinct graphs
AI总结：
该研究证明了在简洁图表示下，某些单称二阶性质要么NP难要么coNP难，并探讨了去除非平凡性条件后的复杂性结果。
摘要：
我们的主要结果是对Courcelle元定理的一个简洁反驳：每种cw非平凡的单称二阶（MSO）性质要么在给定简洁表示的图上是NP难的，要么是coNP难的。简洁表示是通过布尔电路计算邻接关系。Cw非平凡性质是指那些有无限多个模型和无限多个反例且 cliquewidth 有界的性质。此外，我们探讨当去掉cw非平凡性条件时会发生什么，并展示在合理的复杂性假设下，之前的二元分化失效，即使对于可由一阶逻辑表达的问题也是如此。
英文摘要：
Our main result is a succinct counterpoint to Courcelle's meta-theorem as follows: every cw-nontrivial monadic second-order (MSO) property is either NP-hard or coNP-hard over graphs given by succinct representations. Succint representations are Boolean circuits computing the adjacency relation. Cw-nontrivial properties are those which have infinitely many models and infinitely many countermodels with bounded cliquewidth. Moreover, we explore what happens when the cw-nontriviality condition is dropped and show that, under a reasonable complexity assumption, the previous dichotomy fails, even for questions expressible in first-order logic.
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