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A calculus of concurrent graph-rewriting processes
Journal of Logical and Algebraic Methods in Programming ( IF 0.9 ) Pub Date : 2019-10-16 , DOI: 10.1016/j.jlamp.2019.100500
Géza Kulcsár , Andrea Corradini , Malte Lochau

State-of-the-art approaches to controlled graph rewriting focus on the specification of an external control layer over graph-rewriting rule applications and on the input-output semantics of the resulting systems, leading to a decreased relevance of many interesting operational aspects of graph transformation, as studied in the classical theory of algebraic graph rewriting.

We propose a novel approach to controlled graph rewriting where we aim at bridging the gap between these two complementary approaches, defining an operational semantics for which classical concepts and results related to independence and parallelism of graph derivations can be recast.

The calculus we propose is based on a control layer specified using (a fragment of) Milner's Calculus of Communicating Systems (CCS), where the actions specify the application of graph transformation rules to the current state, according to the Double-Pushout approach (DPO).

In particular, we address the following aspects for our controlled graph-rewriting processes: (i) expressiveness of the control language, compared to a minimally complete reference language, Graph Programs, proposed by Habel and Plump; (ii) process equivalence based on labeled transition systems and a structural operational semantics; (iii) a unifying treatment of action independence, considering the corresponding notions from both process algebra and graph-rewriting theory; and (iv) parallelism and concurrency based on the notion of asynchronous (labeled) transition systems, obtained from an asynchronous version of the proposed calculus.



中文翻译:

并发图重写过程的演算

控制图重写的最新技术重点在于图重写规则应用程序上的外部控制层规范以及结果系统的输入输出语义,从而降低了许多有趣的操作方面的相关性图转换,如经典的代数图重写理论所研究。

我们提出了一种新颖的方法来控制图形重写,其目的是弥合这两种互补方法之间的差距,定义一种操作语义,可以重铸与图形派生的独立性和并行性有关的经典概念和结果。

我们建议的演算是基于使用Milner的通信系统演算(CCS)(的一部分)指定的控制层的,其中操作根据Double-Pushout方法(DPO)指定将图变换规则应用于当前状态)。

特别是,我们在控制图形重写过程中解决了以下几个方面:(i)与Habel和Plump提出的最基本的参考语言图形程序相比,控制语言的表现力;(ii)基于标记的过渡系统和结构化操作语义的过程等效性;(iii)统一考虑动作独立性,同时考虑过程代数和图形重写理论中的相应概念;(iv)基于异步(标记的)过渡系统概念的并行性和并发性,该概念是从所提出的演算的异步版本获得的。

更新日期:2019-10-16
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