X Window Implementation of an Algorithm to Synthesize Ordinary Petri Nets

Abstract

平行系統之證明極為複雜，合成法用不著驗證，因此可減輕此複雜度之問題，現今大部分合成技術，並不討論電腦輔助設計，很少的電腦輔助工具具有整合分析、減少、模擬、查詢及合成的能力，派翠圖可模擬及分析平行系統。本人前曾發展－組合成律，可逐漸加大派翠圖，同時確保其邏輯正確無誤。本文指出所合成的派翠圖形成一新的種類，並提出時間矩陣的概念，其可記錄程序間之關係如平行、互斥、及序列。基於這一觀念，吾人發展出演算法，去決定何時可用此合成法，查覺違反此合成法的情況，及重新計算此一矩陣，此演算法之複雜度是Ｏ(Ｋ3)，Ｋ是程序的總數。吾人前所發展之Ｘ視窗工具，以將此演算法具體實踐，此工具可設計、分析，模擬測試及合成通訊協定。

Vertification of concurrent systems faces complexity problem. Synthesis relieves this by avoiding verification. Most existing synthesis techniques do not deal with CAD tool. Few tools are able to integrate analysis, reduction, simulation, query, and synthesis in one software package as ours. Petri nets are used for modelling and analyzing concurrent systems. A set of synthesis rules were developed earlier1-3 for incrementally generating new processes without incurring logical incorrectness. This paper shows that the synthesized nets form a new class of nets and presents the concept of temporal matrix which records relationship (concurrent, exclusive, sequential, ... etc.) among processes. Based on this concept, we develop an algorithm to determinie the applicable rules, detect rule violations, and update the matrix. The complexity for the algorithm is O(K3) where K is the total number of processes. This algorithm has been incorporated int our X-Window based tool for the design, analysis, simulation, testing, and synthesis for communication protocols and others.