Moving a Derivation Along a Derivation Preserves the Spine in Adhesive Categories

Abstract

In this paper, we investigate the relationship between two elementary operations on derivations in the framework of graph transformation based on adhesive categories: moving a derivation along a derivation based on parallel and sequential independence on one hand and restriction of a derivation with respect to a monomorphism into the start object on the other hand. Intuitively, a restriction clips off parts of the start object that are never matched by a rule application throughout the derivation on the other hand. As main result, it is shown that moving a derivation preserves its spine being the minimal restriction.