The Petri Net in Figure 2d models a group of n concurrent processes in a shared

The petri net in figure 2d models a group of n

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Problem 5.The Petri Net in Figure 2(d), models a group ofnconcurrent processes in ashared-memory environment. At any given time only one process may write, but any subsetof thenprocesses may read at the same time, provided that no process writes. Identify thefiring sequences, the markings of the net, the postsets of all transitions and the presets of allplaces. Can you construct a state machine to model the same process? (10) and in this state both read and write operations are permitted. When transition t 2 fires - this represents the initialization of a write request - then the marking becomes M 1 = ( n 1 , 0 , 1 , 0) (11) and neither transition t 1 - which represents the initialization of a read request - nor t 2 can fire, as place p 2 contains no token. This means that only one process can write at a time and no process can read during the write operation. After transition t 3 fires - this represents the actual write operation - the marking becomes the initial one, M 0 . When the system is in state represented by marking M 0 and transition t 1 fires - this represents the initialization of a read request - then the marking becomes M 1 = ( n 1 , n 1 , 0 , 1) (12) and transition t 2 cannot fire - no write can be initialized, but successive n 1 reads can be initiated and then completed. From the state represented by marking M 1 there are two possibilities: 13
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t 4 ( a ) ( b ) ( c ) p 4 t 3 n n n n ( d ) p 1 p 1 p 1 p 1 p 2 p 2 p 2 p 3 p 2 p 3 p 3 p 3 t 1 t 1 t 1 t 1 p 4 p 4 p 4 t 2 t 2 t 2 t 2 t 3 t 3 t 4 t 4 Figure 2: (a) A state machine; there is the choice of firing t 1 , or t 2 ; only one transition fires at any given time, concurrency is not possible. (b) A marked graph can model concurrency but not choice; transitions t 2 and t 3 are concurrent, there is no causal relationship between them. (c) An extended net used to model priorities; the arc from p 2 to t 1 is an inhibitor arc.
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