Analysis of permutation equivalence in -adhesive transformation systems with negative application conditions

M-adhesive categories provide an abstract framework for a large variety of specification frameworks for modelling distributed and concurrent systems. They extend the well-known frameworks of adhesive and weak adhesive HLR categories and integrate high-level constructs like attribution as in the case of typed attributed graphs. This article presents M-adhesive transformation systems including negative application conditions (NACs) for transformation rules, which are often used in applied scenarios. For this purpose, the classical notion of switch equivalence is generalised to the notion of permutation equivalence, because there are intuitively equivalent NAC-consistent transformation sequences which cannot be derived by switching consecutive NAC-independent transformation steps. Furthermore, this article presents a general construction of processes of M-adhesive transformation systems based on subobject transformation systems and permutation equivalence. As main results we show that a constructed process of a transformation sequence specifies its equivalence class of permutation-equivalent transformation sequences. Moreover, we show how the analysis of this process can be reduced to the analysis of the reachability graph of a generated Place/Transition Petri net. This net encodes the dependencies among rule applications of the transformation sequence, including the inhibiting effects of the NACs.