We show that in case a pushdown system is bisimulation equivalent to a finite system, there is already a bisimulation equivalent finite system whose size is elementarily bounded in the description size of the pushdown system. As a consequence we obtain that it is elementarily decidable if a given pushdown system is bisimulation equivalent to some finite system. This improves a previously best-known ACKERMANN upper bound for this problem.

中文翻译：

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下推系统的互模拟有限性是基本的

我们表明，如果下推系统是等效于有限系统的互模拟，则已经存在一个互模拟等价有限系统，其大小基本受限于下推系统的描述大小。因此，我们得到如果给定的下推系统是等效于某个有限系统的互模拟，它是基本可判定的。这改进了这个问题以前最著名的 ACKERMANN 上限。