A Rewriting Calculus for Graphs: Applications to Biology and Autonomous Systems. (Un calcul de réécriture de graphes : applications à la biologie et aux systèmes autonomes)

ions A first-order abstraction in the ρpg-calculus consists of two object port graphs for the leftand the right-hand sides, and an arrow node embedding the correspondence between the two sides. The arrow node has two particular ports, a handler port p0 and a black hole port bh. Some restrictions must be imposed on the connectivity of these two types of ports. A handler port can be connected only to another handler port, and a black hole port can only be the target of an edge whose source is neither a handler port nor a black hole port. Based on Definition 49, an abstraction O1 ⇒ O2 is a port graph constructed as follows: • the arrow node has a port for each port in O1 which is preserved in O2, the black hole port and the handler port; • an edge connects each preserved port p from O1 to their corresponding port of the arrow node which in turn connects to the corresponding ports of p in O2; • the deleted ports from O1 are connected to the black hole. For abstractions of the form (O1 ⇒ O2)⇒ (O′ 1 ⇒ O′ 2), the main arrow node connects ports distinct from the black hole from the main arrow of O1 ⇒ O2 to ports of the main arrow of O′ 1 ⇒ O′ 2 according to the morphism between the two abstractions. The abstractions in A0 are graphically defined as follows: