The theoretician: “Who needs practice? Let’s go home to maths!”

1. theory ? practice theoretical experimental The theoretician: “Who needs practice? Let’s go home to maths!” idealised pragmatic Mathematics study interesting, consistent structures Engineering build practicable, useful structures ComputerScience ?? Carl Adam Petri: “Computing as a science could be modelled after physics” Frederick P. Brooks, Jr.: “The computer “scientist” as toolsmith” Physics predict & measure “real world” structures Christopher Strachey: “.. the separation of practical and theoretical work is artificial and injurious.” Frederick P. Brooks, Jr.: "The scientist builds in order to study, the engineer studies in order to build"

2. Petri Nets Concurrency and causality -a guided tour- Claus Reinke Computing Lab, UKC

3. 3 2 Lift 1 1 Lift 2 Two lifts? From automata ... 3 2 1 Product automaton (meta-level modelling) One lift

4. 3 2 1 Two lifts! … to Petri nets explicit transitions 3 concurrent subsystems 2 explicit synchronisation 1 explicit communication Distributed state, local transitions One lift A passenger local conflict

5. 2 2 max 2 2 2 max 2 2 2 2 2 Lifts again, with place/transition-nets 3 2 1 Two lifts Three passengers two nets, folded in one

6. (l,{p}ps) p (l,ps) (l,ps) p (l,{p}ps) |ps|<2 (l,{p}ps) p (l,ps) (l,ps) p (l,{p}ps) |ps|<2 “keen” (l,{p}ps) p (l,ps) “able” (l,ps) p (l,{p}ps) “quick” (lift1,{}) |ps|<2 (lift2,{}) Lifts, yet again, with high-level nets 3 (l,ps) (l,ps) max 2 (l,ps) (l,ps) max 2 2 (l,ps) (l,ps) (l,ps) (l,ps) 1 Passengers Two lifts