PN-1

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Petri netsrefresher

• Prof.dr.ir. Wil van der Aalst
• Eindhoven University of Technology, Faculty of
  Technology Management,
• Department of Information and Technology, P.O.Box
  513, NL-5600 MB,
• Eindhoven, The Netherlands.

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Elements
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Modeling problem
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Modeling problem (1) Zero testing

• Transition t should fire if place p is empty.

?
t
p
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Solution

• Only works if place is N-bounded

t
Initially there are N tokens
N input and output arcs
p
p
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Modeling problem (2) Priority

• Transition t1 has priority over t2

t1
?
t2
Hint similar to Zero testing!
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A bit of theory

• Extensions have been proposed to tackle these
  problems, e.g., inhibitor arcs.
• These extensions extend the modeling power
  (Turing completeness).
• Without such an extension not Turing complete.
• Still certain questions are difficult/expensive
  to answer or even undecidable (e.g., equivalence
  of two nets).
• Turing completeness corresponds to the ability
  to execute any computation.

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High level Petri netsExtending classical Petri
nets with color, time and hierarchy (informal
introduction)
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Limitations of classical Petri nets

• Inability to test for zero tokens in a place.
• Models tend to become large.
• Models cannot reflect temporal aspects
• No support for structuring large models, cf.
  top-down and bottom-up design

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Inability to test for zero tokens in a place
?
t
p
Tricks only work if p is bounded
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Models tend to become (too) large
Size linear in the number of products.
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Models tend to become (too) large (2)
Size linear in the number of tracks.
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Models cannot reflect temporal aspects
Duration of each phase is highly relevant.
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No support for structuring large models
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High-level Petri nets

• To tackle the problems identified.
• Petri nets extended with
• Color (i.e., data)
• Time
• Hierarchy
• For the time being be do not choose a concrete
  language but focus on the main concepts.
• Later we focus on a concrete language CPN.
• These concepts are supported by many variants of
  CPN including ExSpect, CPN AMI, etc.

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Running example Making punch cards
free desk employees
waiting patients
served patients
patient/ employees
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Extension with color (1)

• Tokens have a color (i.e., a data value)

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Extension with color (2)

• Places are typed (also referred to as color set).

record Brandstring RegistrationNostring
Yearint Colorstring Ownerstring
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Extension with color (3)

• The relation between production and consumption
  needs to be specified, i.e., the value of a
  produced token needs to be related to the values
  of consumed tokens.

The value of the token produced for place sum is
the sum of the values of the consumed tokens.
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Running example Tokens are colored
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Running example Places are typed
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Running example Initial state
start is enabled
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Running example Transition start fired
New value is created by simply merging the two
records.
stop is enabled
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Running example Transition stop fired
New values are created by simply spliting the
record into two parts.