The pebble tree automaton and the pebble tree transducer are enhanced by additionally allowing an unbounded number of “invisible” pebbles (as opposed to the usual “visible” ones). The resulting pebble tree automata recognize the regular tree languages (i.e., can validate all generalized DTD's) and hence can find all matches of MSO definable patterns. Moreover, when viewed as a navigational device, they lead to an XPath-like formalism that has a path expression for every MSO definable binary pattern. The resulting pebble tree transducers can apply arbitrary MSO definable tests to (the observable part of) their configurations, they (still) have a decidable typechecking problem, and they can model the recursion mechanism of XSLT. The time complexity of the typechecking problem for conjunctive queries that use MSO definable patterns can often be reduced through the use of invisible pebbles.

通过额外允许无限数量的“不可见”卵石（与通常的“可见”卵石相对），增强了卵石树自动机和卵石树换能器。生成的pebble树自动机可以识别常规树语言（即可以验证所有通用DTD的语言），因此可以找到MSO可定义模式的所有匹配项。此外，当被视为导航设备时，它们导致了类似于XPath的形式主义，该形式主义具有每个MSO可定义的二进制模式的路径表达式。生成的卵石树换能器可以对它们的配置（可观察的部分）应用任意的MSO可定义的测试，它们（仍然）具有可判定的类型检查问题，并且可以对XSLT的递归机制进行建模。