用结构图分析布尔方程组
Analysis of Boolean Equation Systems through Structure Graphs
摘要：
我们通过使用结构图来分析求解布尔方程组的问题。后者是通过一组优雅的Plotkin风格的演绎规则获得的。本文的主要贡献是证明了具有双相似结构图的方程组具有相同的解。我们表明，我们的工作保守地扩展了早期的工作，由Keiren和Willemse进行，其中依赖图被用来分析布尔方程系统的一个子类，即，标准递归形式的方程组。我们通过一个小例子来说明我们的方法，展示了通过最小化其结构图来简化方程系统的效果。
英文摘要：
We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems with bisimilar structure graphs have the same solution. We show that our work conservatively extends earlier work, conducted by Keiren and Willemse, in which dependency graphs were used to analyse a subclass of Boolean equation systems, viz., equation systems in standard recursive form. We illustrate our approach by a small example, demonstrating the effect of simplifying an equation system through minimisation of its structure graph.
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