A family of tree automata of size n is presented such that the size of the largest common prefix (lcp) tree of all accepted trees is exponential in n. Moreover, it is shown that this prefix tree is not compressible via DAGs (directed acyclic graphs) or tree straight-line programs. We also show that determining whether or not the lcp trees of two given tree automata are equal is coNP-complete; the result holds even for deterministic bottom-up tree automata accepting finite tree languages. These results are in sharp contrast to the case of context-free string grammars.

中文翻译：

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规则树语言的最大通用前缀

给出了一个大小为n的树自动机族，使得所有接受的树中最大的公共前缀（lcp）树的大小在n中是指数的。此外，表明该前缀树无法通过DAG（有向无环图）或树直线程序进行压缩。我们还表明，确定两个给定的树自动机的lcp树是否相等是coNP-complete; 即使对于接受有限树语言的确定性自底向上树自动机，结果也成立。这些结果与无上下文字符串语法的情况形成鲜明对比。