Computing with Graph Relabelling Systems with Priorities

In this paper, the computational power of the noetherian Graph Relabelling systems with Priorities (PGRS for short) is studied. The PGRS's are considered as recognizers for sets of graphs and for sets of 1-sourced graphs. We show that the PGRS's are strictly more powerful for the 1-sourced graphs than for the graphs. Furthermore every set of 1-sourced graphs definable in First Order Logic is recognizable by some PGRS.