Our main result is a polynomial time algorithm for deciding realizability for the GXU sublogic of linear temporal logic. This logic is particularly suitable for the specification of embedded control systems, and it is more expressive than GR(1). Reactive control programs for GXU specifications are represented as Mealy machines, which are extended by the monitoring of input events. Now, realizability for GXU specifications is shown to be equivalent to solving a certain subclass of 2QBF satisfiability problems. These logical problems can be solved in cubic time in the size of GXU specifications. For unrealizable GXU specifications, stronger environment assumptions are mined from failed consistency checks based on Padoa's characterization of definability and Craig interpolation.

翻译：本文的主要结果是一个多项式时间算法，用于判定线性时序逻辑的GXU子逻辑的可实现性。该逻辑特别适用于嵌入式控制系统的规范，且比GR(1)更具表达力。针对GXU规范的响应式控制程序被表示为米利机，并通过输入事件监测进行了扩展。现已证明，GXU规范的可实现性等价于求解某个特定的2QBF可满足性子类问题。这些逻辑问题可在GXU规范规模的立方时间内求解。对于不可实现的GXU规范，基于Padoa可定义性刻画和Craig插值，可从失败的相容性检查中挖掘出更强的环境假设。