petri net (28 slides)
TRANSCRIPT
Petri Net 1
Petri Net:Abstract formal model of information flowMajor use:
Modeling of systems of events in which it is possible for some events to occur concurrently, but there are constraints on the occurrences, precedence, or frequency of these occurrences.
Petri Net 2
Petri Net as a Graph:Models static properties of a system• Graph contains 2 types of nodes
– Circles (Places)– Bars (Transitions)
• Petri net has dynamic properties that result from its execution– Markers (Tokens)– Tokens are moved by the firing of transitions of
the net.
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Petri Net as a Graph (cont.)
(Figure 1) A simple graphrepresentation of a Petri net.
Petri Net 4
Petri Net as a Graph (cont.)
(Figure 2) A markedPetri net.
Petri Net 5
Petri Net as a Graph (cont.)(Figure 3) The marking resulting fromfiring transitiont2 in Figure 2.Note that the token in p1 wasremoved andtokens wereadded to p2 and p3
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Petri Net as a Graph (cont.)(Figure 4) Markings resulting fromthe firing of different transitions in the net of Figure 3.
(a) Result offiring transition t1
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Petri Net as a Graph (cont.)(Figure 4) Markings resulting fromthe firing of different transitions in the net of Figure 3.
(b) Result offiring transition t3
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Petri Net as a Graph (cont.)(Figure 4) Markings resulting fromthe firing of different transitions in the net of Figure 3.
(c) Result offiring transition t5
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Petri Net as a Graph (cont.)
(Figure 5) A simple model of three conditions and an event
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(Figure 6)Modeling of a simplecomputer system
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Petri Net as a Graph (cont.)
(Figure 7) Modeling of a nonprimitive event
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Petri Net as a Graph (cont.)
(Figure 8) Modeling of “simultaneous”which mayoccur in eitherorder
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Petri Net as a Graph (cont.)(Figure 9) Illustration ofconflictingtransitions.Transitions tj
and tk conflictsince thefiring of onewill disablethe other
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Petri Net as a Graph (cont.)(Figure 10) An uninterpretedPetri net.
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(Figure 11) Hierarchicalmodeling in Petri nets byreplacing placesor transitionsby subnets(or vice versa).
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(Figure 12) A portion of aPetri netmodeling acontrol unit fora computer withmultiple registersand multiplefunctional units
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(Figure 13) Representation ofan asynchronouspipelined controlunit. The blockdiagram on the left is modeled bythe Petri neton the right
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Petri Net as a Graph (cont.)
Petri Net 19
(Figure 15)A Petri net model of a P/V solutionto the mutualexclusionproblem
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(Figure 16)Example of a Petri netused to represent theflow of control in programs containingcertain kind of constructs
L: S0
Do while P0
if P2 then S1
else S2
endif parbegin S3,S4,S5, parend enddo goto L
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(Figure 17)A Petri netmodel forprotocol 3
Petri Net 22
Other properties for analysis• Boundeness
– Safe net (bound = 1)– K-bounded net
• Conservation ==> conservative net• Live transition• Dead transition
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State of a Petri net• State - defined by its marking, • State space - set of all markings: (, , , ...)• Change in state - caused by firing a transition,
defined by partial Fn, (example) = ( , tj)
• Note: marking --For a marking , (Pi) = i
A marked Petri net: m = (P, T, I, O, )
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= (1, 0, 1, 0, 2)
(, t3)= (1, 0, 0, 1, 2) = (, t4)= (1, 1, 1, 0, 2) = etc.
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(Figure 19) A Petri netwith anonfirabletransition.Transition t3
is dead inthis marking
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Petri Net as a Graph (cont.)
Petri Net 27
Petri Net as a Graph (cont.)
(Figure 21)The reachability tree of thePetri net ofFigure 19
(1, 0, 1, 0)
(1, 0, 0, 1)
(1, , 1, 0)
(1, , 0, 0) (1, , 0, 1)
(1, , 1, 0)
t3
t2
t1 t3
t2
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Unsolvable Problems• Subset problem - given 2 marked Petri nets, is the
reachability of one net a subset of the reachability of the other net undecidable (Hack) ......
• Complexityreachability problem is exponential time-hard and exponential space-hard.