We present a minimization algorithm for non-deterministic finite state automata that finds and merges bisimulation-equivalent states. The bisimulation relation is computed through partition aggregation, in contrast to existing algorithms that use partition refinement. The algorithm simultaneously generalises and simplifies an earlier one by Watson and Daciuk for deterministic devices. We show the algorithm to be correct and run in time $$ O \left( n^2 r^2 \left| \varSigma \right| \right) $$ O n 2 r 2 Σ , where n is the number of states of the input automaton $$M$$ M , r is the maximal out-degree in the transition graph for any combination of state and input symbol, and $$\left| \varSigma \right| $$ Σ is the size of the input alphabet. The algorithm has a higher time complexity than derivatives of Hopcroft’s partition-refinement algorithm, but represents a promising new solution approach that preserves language equivalence throughout the computation process. Furthermore, since the algorithm essentially computes the maximal model of a logical formula derived from $$M$$ M , optimisation techniques from the field of model checking become applicable.

中文翻译：

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基于聚合的有限状态自动机最小化

我们提出了一种用于非确定性有限状态自动机的最小化算法，它可以找到并合并双模拟等效状态。与使用分区细化的现有算法相比，互模拟关系是通过分区聚合计算的。该算法同时概括和简化了 Watson 和 Daciuk 的早期算法，用于确定性设备。我们证明该算法是正确的并且能及时运行 $$ O \left( n^2 r^2 \left| \varSigma \right| \right) $$ O n 2 r 2 Σ ，其中 n 是状态数在输入自动机 $$M$$ M 中，r 是状态和输入符号的任意组合在转移图中的最大出度，而 $$\left| \varSigma \right| $$ Σ 是输入字母表的大小。该算法比 Hopcroft 的分区细化算法的导数具有更高的时间复杂度，但代表了一种有前途的新解决方案方法，可以在整个计算过程中保持语言等效性。此外，由于该算法本质上是计算从 $$M$$ M 导出的逻辑公式的最大模型，因此模型检查领域的优化技术变得适用。