Virtual symmetry reduction

E. Emerson, John Havlicek, Richard J. Trefler
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引用次数: 40

Abstract

We provide a general method for ameliorating state explosion via symmetry reduction in certain asymmetric systems, such as systems with many similar, but not identical, processes. The method applies to systems whose structures (i.e., state transition graphs) have more state symmetries than arc symmetries. We introduce a new notion of "virtual symmetry" that strictly subsumes earlier notions of "rough symmetry" and "near symmetry" (Emerson and Trefler, 1999). Virtual symmetry is the most general condition under which the structure of a system is naturally bisimilar to its quotient by a group of state symmetries. We give several example systems exhibiting virtual symmetry that are not amenable to symmetry reduction by earlier techniques: a one-lane bridge system, where the direction with priority for crossing changes dynamically; an abstract system with asymmetric communication network; and a system with asymmetric resource sharing motivated from the drinking philosophers problem. These examples show that virtual symmetry reduction applies to a significantly broader class of asymmetric systems than could be handled before.
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虚对称约简
我们提供了一种通过对称约简来改善某些非对称系统状态爆炸的一般方法,例如具有许多相似但不相同过程的系统。该方法适用于结构(即状态转移图)比弧对称具有更多状态对称性的系统。我们引入了一个“虚拟对称”的新概念,它严格地包含了早期的“粗糙对称”和“接近对称”的概念(Emerson和Trefler, 1999)。虚对称是最普遍的条件,在这种条件下,系统的结构与一组状态对称的商自然地双相似。我们给出了几个显示虚拟对称性的系统的例子,这些系统不能通过早期的技术来降低对称性:一个单车道的桥梁系统,其中优先通过的方向是动态变化的;具有非对称通信网络的抽象系统以及一个不对称资源共享的系统,这个系统源于饮酒哲学家的问题。这些例子表明,虚拟对称性约简适用于比以前更广泛的非对称系统。
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