效绵鼎 From automata to Petri Net automata are a theoretical and idealised model they reflect a Newtonian world-view: space time as an absolute frame of reference clockwork view of processes within this frame Carl Adam Petri has made an attempt to combine automata from theoretical CS,and pragmatic expertise from engineers:Petri Net state is distributed,transitions are localised local causality replaces global time subsystems interact by explicit communication
• automata are a theoretical and idealised model • they reflect a Newtonian world-view: • space & time as an absolute frame of reference • clockwork view of processes within this frame • Carl Adam Petri has made an attempt to combine automata from theoretical CS, and pragmatic expertise from engineers: Petri Net From automata to Petri Net • state is distributed, transitions are localised • local causality replaces global time • subsystems interact by explicit communication
效绵鼎 Petri nets-Motivation In contrast to state machines,state transitions in Petri nets are asynchronous.The ordering of transitions is partly uncoordinated;it is specified by a partial order. Therefore,Petri nets can be used to model concurrent distributed systems. Many flavors of Petri nets are in use,e.g. 0 Activity charts(UML) o Data flow graphs and marked graphs 7
Petri nets-Motivation ◼ In contrast to state machines, state transitions in Petri nets are asynchronous. The ordering of transitions is partly uncoordinated; it is specified by a partial order. ◼ Therefore, Petri nets can be used to model concurrent distributed systems. ◼ Many flavors of Petri nets are in use, e.g. Activity charts(UML) Data flow graphs and marked graphs 7
效绵 History 1962:C.A.Petri's dissertation(U.Darmstadt,W.Germany) ■ 1970:Project MAC Conf.on Concurrent Systems and Parallel Computation(MIT,USA) 1975:Conf.on Petri Nets and related Methods(MIT,USA) 1979:Course on General Net Theory of Processes and Systems (Hamburg,W.Germany） 1980:First European Workshop on Applications and Theory of Petri Nets (Strasbourg,France) 1985:First International Workshop on Timed Petri Nets(Torino,Italy)
History ◼ 1962: C.A. Petri’s dissertation (U. Darmstadt, W. Germany) ◼ 1970: Project MAC Conf. on Concurrent Systems and Parallel Computation (MIT, USA) ◼ 1975: Conf. on Petri Nets and related Methods (MIT, USA) ◼ 1979: Course on General Net Theory of Processes and Systems (Hamburg, W. Germany) ◼ 1980: First European Workshop on Applications and Theory of Petri Nets (Strasbourg, France) ◼ 1985: First International Workshop on Timed Petri Nets (Torino, Italy)
效绵县 Introduction Petri Nets:Graphical and Mathematical modeling tools 0 graphical tool ■ visual communication aid o mathematical tool state equations,algebraic equations,etc concurrent,asynchronous,distributed,parallel, nondeterministic and/or stochastic systems
Introduction ◼ Petri Nets: Graphical and Mathematical modeling tools graphical tool ◼ visual communication aid mathematical tool ◼ state equations, algebraic equations, etc ◼ concurrent, asynchronous, distributed, parallel, nondeterministic and/or stochastic systems
效绵 Informal Definition ■ The graphical presentation of a Petri net is a bipartite graph There are two kinds of nodes o Places:usually model resources or partial state of the system o Transitions:model state transition and synchronization Arcs are directed and always connect nodes of different types Tokens are resources in the places
Informal Definition ◼ The graphical presentation of a Petri net is a bipartite graph ◼ There are two kinds of nodes Places: usually model resources or partial state of the system Transitions: model state transition and synchronization ◼ Arcs are directed and always connect nodes of different types ◼ Tokens are resources in the places