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Unformatted text preview: Introduction to Petri Nets II Anders Moen 1 Introduction to Petri Nets  Part Two Anders Moen March 26, 2003 1 Introduction to Petri Nets II Anders Moen 2 In this Crash course we present • Elementary Nets • Place Transition Nets • Coloured Petri Nets This time we continue with EN systems and proceed into Place Transition nets. Now we shall have lots of fun! Important references: http://heim.ifi.uio.no/~andersmo/petrinet.html Introduction to Petri Nets II Anders Moen 3 Repetition from last time Our first Petri Net see Figure 4: p1 t1 p2 t3 p4 p5 t2 t4 Producer Consumer Buffer p3 A Petri Net consists basically of four components • Places • Transitions • Arcs • Tokens Last time we learned about markings of nets, enabling and firing of transitions in a sequential setting. Today we shall learn about much more! Definition 1 Let S = h P, T, F, M in i be an elementary nets system. We say that the underlying graph of N , is the elemantary net of N, that is; graph ( N ) = h P, T, F i . Somebody also writes und , for the underlying graph of an elementary nets system. Introduction to Petri Nets II Anders Moen 4 Marking graphs We recapitulate the exercise from last time to give the marking graph (occurence graph) of the previous Consumer Producer elementary net system. Then we draw the marking graph, as you can see to the left: p1 p3 p4 p2 p3 p4 p1 p2 t1 t2 t2 t1 p2 p5 p1 p4 t4 t1 t4 p2 p4 p1 p3 p5 t3 t1 p2 p3 p5 t4 t4 t3 p1 t1 p2 t3 p4 p5 t2 t4 Producer Consumer Buffer p3 Exercise 1 Let S be an EN system S = h P, T, F, M in i where graph (S), is Producer consumer example. Consider now other initial marking than M in to get new elementary net systems S 1 = h P, T, F, M 1 in i and S 2 = h P, T, F, M 2 in i : Let M 1 in = { p 2 , p 5 } and M 2 in = { p 4 , p 5 } . What are the sequential marking graphs of S 1 and S 2 ? Introduction to Petri Nets II Anders Moen 5 Concurrency Petri Nets are true concurrent. The semantics of elementary nets permit events (firing of transitions) to happen at the same time. Definition 2 Let S = h P, T, F, M in i be an elementary nets system, And let U be a subset of all the transitions of S , U ⊆ T . Then we say that U is a disjoint set of transition if 1. U 6 = ∅ 2. ∀ t 1 ∈ U ∀ t 2 ∈ U ( t 1 6 = t 2 → nbh ( t 1 ) ∩ nbh ( t 2 ) = ∅ ) When U is a disjoint set of transition, we write disj ( U ) Exercise 2 In Produceer Consumer example, there are 4 transitions. How many sets of transitions can you make? Write them down. Which of the sets are disjoint sets of transitions? Definition 3 Let S be an EN system as above. Let U ⊆ T be a set of transitions, and M ⊆ P a marking. Then the set of transitions U is generally enabled in M if: 1. U is a disjoint set of transition, disj ( U ) ....
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This note was uploaded on 12/28/2010 for the course ACC 320 taught by Professor Dr.merker during the Spring '10 term at London College of Accountancy.
 Spring '10
 Dr.Merker

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