大型布尔方程研究进展综述
An Overview of Recent Developments in Big Boolean Equations
摘要：
求解大型布尔方程组的方法大致可分为代数法、表格法、数值法和地图法。这些类中最突出的是代数方法和映射方法。本文调查和比较这两种方法的简单性，效率和可用性。本文将布尔方程的解分为包含通解、参数通解和特解三类。在包含通解中，每个变量都表示为基于原函数的连续合取或析取消去式的区间。在参数通解中，每个变量都是通过任意参数来表示的，这些参数是基础布尔代数的自由选择的元素。一个特殊的解决方案是从底层布尔代数到每个相关变量的赋值，使布尔方程成为恒等式。本文提供了一个教程的阐述，审查和比较的三种类型的解决方案，通过一个说明性的例子。这个例子也是从最近开发的依赖于原子分解的技术的角度来看的。地图技术被证明是至少有竞争力的（有时优于）代数技术，因为他们有一个更好的控制最小的相关功能表示，因此更能够产生更紧凑的解决方案。
英文摘要：
Methods of solving big Boolean equations can be broadly classified as algebraic, tabular, numerical and map methods. The most prominent among these classes are the algebraic and map methods. This paper surveys and compares these two types of methods as regards simplicity, efficiency, and usability. The paper identifies the main types of solutions of Boolean equations as subsumptive general solutions, parametric general solutions and particular solutions. In a subsumptive general solution, each of the variables is expressed as an interval based on successive conjunctive or disjunctive eliminants of the original function. In a parametric general solution each of the variables is expressed via arbitrary parameters which are freely chosen elements of the underlying Boolean algebra. A particular solution is an assignment from the underlying Boolean algebra to every pertinent variable that makes the Boolean equation an identity. The paper offers a tutorial exposition, review, and comparison of the three types of solutions by way of an illustrative example. This example is also viewed from the perspective of a recently developed technique that relies on atomic decomposition. Map techniques are demonstrated to be at least competitive with (and occasionally superior to) algebraic techniques, since they have a better control on the minimality of the pertinent function representations, and hence are more capable of producing more compact solutions.
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。
