Thierry Boy de la Tour

Thierry Boy de la Tour

An Independent Parallelism Theorem is proven in the theory of adhesive HLR categories. It shows the bijective correspondence between sequential independent and parallel independent direct derivations in the Weak Double-Pushout framework, see [2]. The parallel derivations are expressed by means of Parallel Coherent Transformations (PCTs), hence without assuming the existence of coproducts compatible with M as in the standard Parallelism Theorem. It is aslo shown that a derived rule can be extracted from any PCT, in the sense that to any direct derivation of this rule corresponds a valid PCT.

Thierry Boy de la Tour, Rachid Echahed

We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the form $L\xleftarrow{l}K \xleftarrow{i} I \xrightarrow{r} R$, called weak spans. A parallel coherent transformation is introduced and shown to be a conservative extension of the interleaving semantics of parallel independent direct transformations. A categorical construction of finitely attributed structures is proposed, in which parallel coherent transformations can be built in a natural way. These notions are introduced and illustrated on detailed examples.