求解正则方程再访（扩展版）
Solving of Regular Equations Revisited (extended version)
摘要：
用阿登引理求解正则方程是一门民间知识。我们首先给出一个简明的算法规范的所有基本的解决步骤。然后，我们讨论了一个计算解释的解决方案的解析树转换成解析树的解决方案的正则方程的解析子。因此，我们可以确定正则方程的形状的一些条件下，得到的解决方案是明确的。我们应用我们的结果将DFA转换为一个明确的正则表达式。此外，我们表明，如减法和洗牌操作可以表示通过一些适当的一组正则方程。因此，我们得到直接（代数）方法，而不必转换到和从有限自动机。
英文摘要：
Solving of regular equations via Arden's Lemma is folklore knowledge. We first give a concise algorithmic specification of all elementary solving steps. We then discuss a computational interpretation of solving in terms of coercions that transform parse trees of regular equations into parse trees of solutions. Thus, we can identify some conditions on the shape of regular equations under which resulting solutions are unambiguous. We apply our result to convert a DFA to an unambiguous regular expression. In addition, we show that operations such as subtraction and shuffling can be expressed via some appropriate set of regular equations. Thus, we obtain direct (algebraic) methods without having to convert to and from finite automaton.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
