带确定性ε-转移的下推系统的弱双模拟有限性是2-ExpTime完全的
Weak Bisimulation Finiteness of Pushdown Systems With Deterministic $\varepsilon$-Transitions Is 2-ExpTime-Complete
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中文总结 AI 辅助
本文证明带确定性ε-转移的下推系统的弱双模拟有限性问题是2-ExpTime完全的，给出了有限系统规模的双指数上界、判定算法及困难性证明，改进了此前的复杂度结果。
中文摘要 AI 辅助
我们研究的问题是：判定给定的所有ε-转移均为确定性的下推系统是否是弱双模拟有限的，即该系统是否与某个有限系统弱双模拟等价。我们证明该问题是2-ExpTime完全的，这包含三个部分：第一，证明与固定下推系统弱双模拟等价的最小有限系统（若存在），其规模至多为下推系统描述规模的双指数级；第二，提出一种快速算法，用于判定给定下推系统是否与给定规模的有限系统弱双模拟等价；第三，证明该问题的2-ExpTime困难性。此前已知该问题可判定，但已有算法具有阿克曼复杂度（对于无ε-转移的下推系统这一更简单情况，复杂度为6-ExpSpace）；关于下界，此前仅知其为ExpTime困难的。
英文摘要
We consider the problem of deciding whether a given pushdown system all of whose $\varepsilon$-transitions are deterministic is weakly bisimulation finite, that is, whether it is weakly bisimulation equivalent to a finite system. We prove that this problem is 2-ExpTime-complete. This consists of three elements: First, we prove that the smallest finite system that is weakly bisimulation equivalent to a fixed pushdown system, if exists, has size at most doubly exponential in the description size of the pushdown system. Second, we propose a fast algorithm deciding whether a given pushdown system is weakly bisimulation equivalent to a finite system of a given size. Third, we prove 2-ExpTime-hardness of the problem. The problem was known to be decidable, but the previous algorithm had Ackermannian complexity (6-ExpSpace in the easier case of pushdown systems without $\varepsilon$-transitions); concerning lower bounds, only ExpTime-hardness was known.
