Processes and unfoldings: concurrent computations in adhesive categories
Processes and unfoldings: concurrent computations in adhesive categories
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过程和展开：粘合剂类别中的并发计算
DOI：
10.1017/s096012951200031x
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发表时间：
2014
影响因子：
0.5
通讯作者：
P. Sobocinski
中科院分区：
文献类型：
--
作者：
Paolo Baldan;A. Corradini;T. Heindel;B. König;P. Sobocinski
我们概括的概念，一个非顺序的过程和展开的建设（这是以前开发的具体形式主义，如Petri网和图形语法）的抽象设置（单推出）重写对象的粘合剂类别。主要结果表明，过程是在一对一的对应关系与开关等价类的衍生物，和展开建设的特点是作为一个coreflection，即展开函子出现的权利伴随到发生语法的类别嵌入到类别的语法。由于展开表示潜在的无限计算，我们需要在具有monos的ω-链的“行为良好”的共极限的粘附范畴中工作。与以前的工作相比，展开的Petri网和图形语法，我们的研究结果适用于更广泛的一类系统，这是由于使用了一个精致的概念，语法态射。
We generalise both the notion of a non-sequential process and the unfolding construction (which was previously developed for concrete formalisms such as Petri nets and graph grammars) to the abstract setting of (single pushout) rewriting of objects in adhesive categories. The main results show that processes are in one-to-one correspondence with switch-equivalent classes of derivations, and that the unfolding construction can be characterised as a coreflection, that is, the unfolding functor arises as the right adjoint to the embedding of the category of occurrence grammars into the category of grammars. As the unfolding represents potentially infinite computations, we need to work in adhesive categories with ‘well-behaved’ colimits of ω-chains of monos. Compared with previous work on the unfolding of Petri nets and graph grammars, our results apply to a wider class of systems, which is due to the use of a refined notion of grammar morphism.