Petri Nets Lecture 1. Chen Chen Sep. 28 th, /9/28 \course\867-11f\topic-2.ppt 1
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1 Petri Nets Lecture 1 Chen Chen Sep. 28 th, /9/28 \course\867-11f\topic-2.ppt 1
2 Outline History of Petri Nets Basic Terminologies Comparing with FSM Petri Net Properties 2011/9/28 \course\867-11f\topic-2.ppt 2
3 Invention of Petri Nets C.A. Petri (1962). Kommunikation mit Automaten. Ph. D. Thesis. University of Bonn. IEEE Computer Pioneer Award (2008) For establishing Petri net theory in 1962, which not only was cited by hundreds of thousands of scientific publications but also significantly advanced the fields of parallel and distributed computing Carl Adam Petri /9/28 \course\867-11f\topic-2.ppt 3
4 Introduction to Petri Nets Theory A theory of systems for modeling concurrency and synchronization Feature Graphical representation Simplicity Expressiveness for concurrency and asynchronous operations 2011/9/28 \course\867-11f\topic-2.ppt 4
5 History of Petri Nets Hack (1972) Free-choice Petri Nets Simple Petri Nets R. David & H. Alla (1987) Continuous Petri Nets Chiola, Dutheillet, Franceschinis, S. Haddad. (1991) Well-Formed Coloured Nets ISO/IEC (2011) Petri Nets Standard Holt and Commoner (1970) Graphical expression of PN Marked Graph Kurt Jensen (1981) Colored Petri Nets Bail, Alla, David (1991) Hybrid Petri Nets Rudiger Valk (1998) Elementary Object Nets Haddad & Poitrenaud (2007) Recursive Petri Nets C.A. Petri (1962) Invention of Petri Nets First PN Sub-class of PN Ramchandani (1973) Timed Petri Nets M.K. Molly (1982) Stochastic Petri Nets Extension of PN Normalization of PN Buchs and Guelfi (1991) Object Oriented Petri Net E. P. Dawis, J. F. Dawis, Wei-Pin Koo(2001) Dualistic Petri Nets 2011/9/28 \course\867-11f\topic-2.ppt 5
6 Outline History Basic Terminologies Comparing with FSM Petri Net Properties 2011/9/28 \course\867-11f\topic-2.ppt 6
7 Example: Critical Section 3 users try to access the same CS Only one user can access CS each time 1 token = lock place p 3 3 tokens = 3 users t 1 transition Critical Section p 1 p 2 arc t 2 token 2011/9/28 \course\867-11f\topic-2.ppt 7
8 Example: Critical Section Multiple users try to access the same CS Only one user can access CS each time p 3 p 3 p 2 p 1 t 1 t 2 t 1 One user entered CS p 1 p 2 The others have to wait t /9/28 \course\867-11f\topic-2.ppt 8
9 Example: Critical Section Multiple users try to access the same CS Only one user can access CS each time p 3 p 3 p 3 p 2 p 1 t 1 p 2 p 1 t 1 p 2 p 1 t 1 t 2 t 2 t 2 One user completes access. Another one can enter now. 2011/9/28 \course\867-11f\topic-2.ppt 9
10 Example: Producer-Consumer Producer Task Buffer Consumer A Consumer B Producer produces tasks and put the tasks in the task buffer. Consumers take tasks from the task buffer and execute them. One task can only be executed by one consumer either A or B. 2011/9/28 \course\867-11f\topic-2.ppt 10
11 Example: Producer-Consumer Producer Task Buffer Consumer A Consumer B Producer produced one task. Either A or B can be fired. But only one will be fired! 2011/9/28 \course\867-11f\topic-2.ppt 11
12 Example: Producer-Consumer Producer Task Buffer Consumer A Consumer B After firing A or B, the task is executed. 2011/9/28 \course\867-11f\topic-2.ppt 12
13 Example: Producer-Consumer Producer Task Buffer What will happen after token pushing? Consumer A Petri Nets Consumer B Dataflow (similar structure but different semantics) What s the difference between Petri Nets and Dataflow? 2011/9/28 \course\867-11f\topic-2.ppt 13
14 Definition of a Petri Net (Self-reading) A Petri Net is a bipartite graph (P,T,A) that comprises of A set of transitions: T A set of places: P A set of directed arcs: A a transition a place 2011/9/28 \course\867-11f\topic-2.ppt 14
15 Firing Rules (Self-reading) 2011/9/28 \course\867-11f\topic-2.ppt 15
16 Petri Net Marking (Selfreading) 2011/9/28 \course\867-11f\topic-2.ppt 16
17 Outline History Basic Terminologies Comparing with FSM Petri Net Properties 2011/9/28 \course\867-11f\topic-2.ppt 17
18 Example: Two s Complement What is two s complement? How to compute two's complement? 2011/9/28 \course\867-11f\topic-2.ppt 18
19 Example: Two's Complement (cont.) What is two's complement? How to compute two's complement? flip all bits, and then plus a carry bit Assume B = 110, then -B = = /9/28 \course\867-11f\topic-2.ppt 19
20 Example: Two's Complement (cont.) What is two's complement? How to compute two's complement? flip all bits, and then plus a carry bit Assume B = 110, then -B = = 010 Compute two's complement of 110 from low bit flip(0) + carry bit = 0 & carry bit flip(1) + carry bit = 1 flip(1) /9/28 \course\867-11f\topic-2.ppt 20
21 Example: Two's Complement (cont.) 0/0 0/1 1/1 q 1 q 2 R means reset of computation R/R R/R 1/0 State q 1 : need to add carry bit flip(0) + carry bit = 0 + carry bit flip(1) + carry bit = 1 State q 2 : no need to add carry bit flip(0) 1 flip(1) /9/28 \course\867-11f\topic-2.ppt 21
22 Example: FSM (cont.) 0/0 1/1 0/1 q 1 q 2 R/R R/R 1/0 Now try to compute two's complement of /9/28 \course\867-11f\topic-2.ppt 22
23 Example: FSM (cont.) /0 1/1 0/1 q 1 q 2 R/R R/R 1/0 Two's complement of 110 is /9/28 \course\867-11f\topic-2.ppt 23
24 Example: FSM (cont.) Input sequence : R11 Output sequence: 0 0/0 1/1 0/1 Computing from low bit R indicates reset q 1 q 2 R/R R/R 1/0 Two's complement of 110 is /9/28 \course\867-11f\topic-2.ppt 24
25 Example: FSM (cont.) Input sequence : R1 Output sequence: 10 0/0 1/1 0/1 Computing from low bit R indicates reset q 1 q 2 R/R R/R 1/0 Two's complement of 110 is /9/28 \course\867-11f\topic-2.ppt 25
26 Example: FSM (cont.) Input sequence : R Output sequence: 010 0/0 1/1 0/1 Computing from low bit R indicates reset q 1 q 2 R/R R/R 1/0 Two's complement of 110 is /9/28 \course\867-11f\topic-2.ppt 26
27 Example: FSM (cont.) /0 1/1 0/1 q 1 q 2 R/R R/R 1/0 Two's complement of 110 is /9/28 \course\867-11f\topic-2.ppt 27
28 Finite State Machine (FSM) Self-reading 2011/9/28 \course\867-11f\topic-2.ppt 28
29 Important Features of FSM What are the features? 2011/9/28 \course\867-11f\topic-2.ppt 29
30 Important Features of FSM What are the features? FSM is always at a single active state! A single input event triggers state transition! 2011/9/28 \course\867-11f\topic-2.ppt 30
31 Important Features of FSM What are the features? FSM is always at a single active state! How to represent multiple active states as a single active state? A single input event triggers state transition! How to represent synchronization between multiple states? 2011/9/28 \course\867-11f\topic-2.ppt 31
32 Another Example: 2-Stage Pipeline Modeling Input sequence Output sequence Unit1 Unit2 Unit I (I = 1,2) busy ready to output Each unit can be modeled by a three-state FSM b a c ready for input 2011/9/28 \course\867-11f\topic-2.ppt 32
33 Another Example: 2-Stage Pipeline Modeling (cont.) Input sequence Output sequence Unit1 Unit2 How to model the two units together in FSM? 2011/9/28 \course\867-11f\topic-2.ppt 33
34 Another Example: 2-Stage Pipeline Modeling (cont.) Input sequence Output sequence Unit1 Unit2 How to model the two units together in FSM? cross-functional states State aa : Unit1 is ready for input & Unit2 is ready for input State ba : Unit1 is busy & Unit2 is ready for input State ca : Unit 1 is ready to output & Unit2 is ready for input State cc : Unit 1 is ready to output & Unit 2 is ready to output 2011/9/28 \course\867-11f\topic-2.ppt 34
35 Another Example: 2-Stage Pipeline Modeling (cont.) ab aa ac ba ca bb cc bc The structure of the FSM for 2-stage pipeline modeling. Inputs and outputs are omitted. 2011/9/28 \course\867-11f\topic-2.ppt 35 cb
36 Problems of FSM Modeling of the Pipeline Number of states grows exponentially with the number of stages The identity of the individual stage lost The structure information is obscured Concurrency / synchronization information cannot be represented 2011/9/28 \course\867-11f\topic-2.ppt 36
37 Try Again: 2-Stage Pipeline Modeling by PN Input sequence Output sequence Unit1 Unit2 Unit I (I = 1,2) Done with processing busy ready to output Each unit can be modeled by 3 places and 3 transitions Output result Pickup input data ready for input 2011/9/28 \course\867-11f\topic-2.ppt 37
38 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Input sequence Unit1 Output sequence Unit2 Pipeline Done with processing Done with processing PN busy busy ready to output ready to output Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input 2011/9/28 \course\867-11f\topic-2.ppt 38
39 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Unit1 Done with processing Unit2 Done with processing busy ready to output ready to output busy Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input Scenario: D1 in the entrance of Unit1 D2 in the entrance of Unit1 2011/9/28 \course\867-11f\topic-2.ppt 39
40 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Unit1 Done with processing Unit2 Done with processing busy ready to output ready to output busy Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input Scenario: D1 being processed by Unit1 D2 in the entrance of Unit1 2011/9/28 \course\867-11f\topic-2.ppt 40
41 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Unit1 Done with processing Unit2 Done with processing busy ready to output ready to output busy Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input Scenario: D1 is done by Unit1 D2 in the entrance of Unit1 2011/9/28 \course\867-11f\topic-2.ppt 41
42 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Unit1 Done with processing Unit2 Done with processing busy ready to output ready to output busy Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input Scenario: D1 being processed by Unit2 D2 in the entrance of Unit1 2011/9/28 \course\867-11f\topic-2.ppt 42
43 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Unit1 Done with processing Unit2 Done with processing busy ready to output ready to output busy Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input Scenario: D1 is done by Unit2 D2 being processed by Unit1 2011/9/28 \course\867-11f\topic-2.ppt 43
44 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Unit1 Done with processing Unit2 Done with processing busy ready to output ready to output busy Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input Scenario: Result of D1 is outputted by Unit2 D2 is done by Unit1 2011/9/28 \course\867-11f\topic-2.ppt 44
45 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Unit1 Done with processing Unit2 Done with processing busy ready to output ready to output busy Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input Scenario: Result of D1 is outputted by Unit2 D2 being processed by Unit2 2011/9/28 \course\867-11f\topic-2.ppt 45
46 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Unit1 Done with processing Unit2 Done with processing busy ready to output ready to output busy Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input Scenario: Result of D1 is outputted by Unit2 D2 is done by Unit2 2011/9/28 \course\867-11f\topic-2.ppt 46
47 Try Again: 2-Stage Pipeline Modeling by PN (cont.) Unit1 Done with processing Unit2 Done with processing busy ready to output ready to output busy Output result Pickup input data ready for input Unit1 transfers intermediate result to Unit2 ready for input Scenario: Result of D1 is outputted by Unit2 Result of D2 is outputted by Unit2 2011/9/28 \course\867-11f\topic-2.ppt 47
48 Conclusion: Compare PN with FSM PN is powerful in constructing composite machines. FSM must do cross product. PN is powerful in expressing concurrency. (FSM cannot express concurrency). PN is powerful in expressing synchronization. 2011/9/28 \course\867-11f\topic-2.ppt 48
49 Outline History Basic Terminologies Comparing with FSM Petri Net Properties 2011/9/28 \course\867-11f\topic-2.ppt 49
50 Petri Net Properties Reachability Safeness and Boundness Conservation Liveness Persistency Consistency 2011/9/28 \course\867-11f\topic-2.ppt 50
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