Extensive optimizing and parallelizing transformations are carried out on programs, both by (untrusted) compilers and human experts, before deploying them on some platform architecture which is by and large parallel. It is therefore important to devise some suitable modelling paradigm which is capable of capturing parallelism in such a way that proving equivalence of the source programs and their transformed versions becomes easier. In the present work, an untimed Petri net model with data constraints, called CPN model (Coloured Petri net), is used to model the parallel behaviours. Being value based, such models depict more vividly the data dependencies which lie at the core of such transformations; accordingly, they are likely to provide more suitable internal representations (IRs) of both the source and the transformed programs than the IRs like sequential control flow graphs (CFGs). A path based equivalence checking method for CPN models with rigorous treatment of the complexity and correctness issues have been presented. Experimental results show the effectiveness of the approach.

中文翻译：

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使用静态和动态切点对程序的 Petri 网模型进行等价检查

广泛的优化和并行化转换由（不受信任的）编译器和人类专家在程序上执行，然后再将它们部署到一些大体上并行的平台架构上。因此，重要的是设计一些合适的建模范式，该范式能够以这样的方式捕获并行性，从而更容易证明源程序及其转换版本的等效性。在目前的工作中，一个具有数据约束的非定时 Petri 网模型，称为 CPN 模型（彩色 Petri 网），用于模拟并行行为。由于基于价值，此类模型更生动地描述了作为此类转换核心的数据依赖关系；因此，与顺序控制流图 (CFG) 等 IR 相比，它们可能会提供更合适的源程序和转换后的程序的内部表示 (IR)。提出了一种基于路径的 CPN 模型等价检查方法，严格处理复杂性和正确性问题。实验结果表明了该方法的有效性。