Tutorial Abstract

Many systems are made of components, connectors and wires, can evolve in parallel/concurrently with limited, local reconfiguration and have interfaces through which they can be observed and composed.

Lots of models have been proposed for them. Examples: (i) Petri nets; (ii) linear time-invariant dynamical systems; (iii) (soft) constraint satisfaction problems; (iv) Bayesian networks; (v) electric circuits; (vi) bigraphs; (vii) computational fields.

General approaches have been proposed for describing such systems. We distinguish three of them:

• Milner flowgraphs: networks of constraints; treewidth decomposition for dynamic programming; interpreted flow algebras; synchronized hyperedge replacement systems.
• PROPs and string diagrams: connector algebras for nets with boundaries; signal flow graphs; bigraphs.
• From graphs to categories: Petri nets and monoidal categories; rewriting logic; tiles.