自動化系統常見於日常生活中，可程式邏輯控制器(Programmable Logic Controller, PLC)為其控制手段之一，階梯圖(Ladder Diagram, LD)則為常用的PLC編程方法。一個自動化系統必須歷經規格、驗證、撰碼、測試與偵查五項步驟，然而階梯圖不易系統化建構與偵錯，為加速其開發流程，我們可先以易於描述離散型系統動態行為的裴氏圖(Petri Net, PN)建構，經過分析驗證後再轉換為對應的階梯圖。

在階梯圖的設計過程中，常會因編程人員的疏失而導致系統中的某個或多個工件彼此佔住資源，互相等待其它工件釋放資源而本身卻不釋放資源的「鎖死」(Deadlock)現象。此時若將階梯圖轉換為裴氏圖即可較易進行「鎖死分析」(Deadlock Analysis)，以找出並解決鎖死現象。基於裴氏圖的鎖死分析有裴氏圖的結構分析(基於Siphon的方法)與可達圖(Reachability Graph)分析等兩種手法，本研究擬應用區域理論(Theory of Region)與可達圖來分析鎖死問題，並運用裴氏圖化簡方法，降低產生可達圖時因裴氏圖的規模增加而導致的狀態數爆增問題。最後透過裴氏圖軟體Petri LLD將無鎖死的裴氏圖再轉換回階梯圖，以塑膠射出成型機為例，實現自動化系統建構的程序。

The Ladder diagram is the most popular programming language for the programmable logic controller (PLC) that is commonly used in controlling an automatic system. The Ladder diagram programmers usually suffer from the problem of deadlocks in which two or more competing processes waiting for each other to finish, and thus none of them continues. The deadlock problem of a ladder diagram is difficult to be detected and resolved, yet it is easier to conduct the deadlock analysis over the Petri net associated with a ladder diagram. We use the theory of region and the reachability graph to analyze deadlocks. By techniques of Petri net reduction, we could avoid the problem of state explosion for large-scale Petri nets. After resolving the deadlocks, we convert a deadlock-free Petri net back to a Ladder diagram. We illustrate how these procedures work by several real-world examples.

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