$mathcal{M}$-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation
$mathcal{M}$-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation
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$mathcal{M}$-具有嵌套应用条件的粘合转换系统。
DOI：
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发表时间：
2014
影响因子：
0.5
通讯作者：
F. Orejas
中科院分区：
文献类型：
--
作者：
H. Ehrig;Ulrike Golas;A. Habel;Leen Lambers;F. Orejas
嵌套的应用条件概括了众所周知的负面应用条件，对几个应用领域很重要。本文在$mathcal{M}$-粘附范畴的框架下，给出了应用条件嵌套规则的局部Church-Rosser定理、并行定理、并发定理和归并定理，其中$mathcal{M}$-粘附范畴比弱粘附高级替换范畴更一般.大多数的证明是基于相应的陈述规则没有应用条件和两个移位引理，说明嵌套的应用条件可以转移到态射和规则。
Nested application conditions generalise the well-known negative application conditions and are important for several application domains. In this paper, we present Local Church–Rosser, Parallelism, Concurrency and Amalgamation Theorems for rules with nested application conditions in the framework of $mathcal{M}$-adhesive categories, where $mathcal{M}$-adhesive categories are slightly more general than weak adhesive high-level replacement categories. Most of the proofs are based on the corresponding statements for rules without application conditions and two shift lemmas stating that nested application conditions can be shifted over morphisms and rules.