non-ZenoAndAcceptingLocation

PATTERN系列的番外篇
对non-Zeno的概念进行了明晰

accepting：if infinitely often the same state

non-Zeno：if time diverges，which means \(\sum_{i\geq20}\)\(\delta_{i}\) \(\rightarrow \infin\)

Abstract zone graphs again：

​ Extra\(^{+}_{LU}\)

​ \(\nearrow\) \(\nwarrow\)

​ Extra\(^{+}_{M}\) Extra\(_{LU}\)

​ \(\nwarrow\) \(\nearrow\)

​ Extra\(_{M}\)

ZG^a^\(( \mathcal{A} )\) ：(\(q_0\)\(,\) \(Z_0\))\(\rightarrow\)(\(q_1\)\(,\) \(Z_1\))\(\rightarrow\) (\(q_2\)\(,\) \(Z_2\))\(\rightarrow\)\(\cdots\)

​ \(\mathcal{A}\)：(\(q_0\)\(,\) \(v_0\))\(\rightarrow\) (\(q_1\)\(,\) \(v_1\))\(\rightarrow\) (\(q_2\)\(,\) \(v_2\))\(\rightarrow\)\(\cdots\)

（All the above abstractions preserve repeated state reachability）

其中\(\mathcal{A}\)中的每一个状态都是ZG^a^\(( \mathcal{A} )\) 中相应状态的元素，即 \(\forall i\geq0\) 有\(v_i\) \(\in\) \(Z_i\)

Time progress criterion： \(\bigwedge_{x \in X}\)unbounded\((x)\)\(\vee\)fluctuating\((x)\)

non-Zenoness： the time progress criterion is not sound on zones

note: Adding one clock leads to an exponential blowup in the zone graph!

​ exponential blowup：指数爆炸