INFORMATIESYSTEMEN
SA M E N VAT T I N G
+,-.-+,+,
I N H O U D S O P G AV E
College 1: Labeled Transitie Systemen ................................................................................................................. 3
College 2: Grafen doorzoeken ............................................................................................................................... 7
2.1 Breadth First Search ...................................................................................................................................... 7
2.2 Depth First Search ......................................................................................................................................... 8
2.3 Dijkstra’s shortest path algorithm ................................................................................................................. 9
College 3: Informatiemodellen ............................................................................................................................ 11
It’s a True World ................................................................................................................................................ 11
College 4: BPM (I) ................................................................................................................................................ 15
Ingrediënten van het BPMN-proces ................................................................................................................... 15
BPM-lifecycle: .................................................................................................................................................... 15
College 5: Synchroon Product en Inleiding Petrinetten .................................................................................... 16
5.1 Synchroon product ....................................................................................................................................... 16
5.2 Using The Synchronous Product in modeling .............................................................................................. 18
5.3 Informal Introduction to Petri Nets .............................................................................................................. 20
5.4 Modeling with Petri Nets.............................................................................................................................. 20
College 6: Modeling with Petri Nets.................................................................................................................... 22
6.1 Formal Definition of Petri Nets.................................................................................................................... 22
6.2 Extending Petri Nets with Arc Weights ........................................................................................................ 24
College 7: Bpm-basic modelling .......................................................................................................................... 25
BPMN vertalen naar Petri net............................................................................................................................ 25
College 8: Petrinetten III...................................................................................................................................... 26
8.1 Reachability Graphs and Petri nets ............................................................................................................. 26
8.2 Petri Net Classes .......................................................................................................................................... 28
College 9: Petrinetten met Data........................................................................................................................... 33
9.1 Colored Petri nets ........................................................................................................................................ 33
, 9.2 Petri nets with identifiers ............................................................................................................................. 34
College 10: Informatiesysteemmodelleren ......................................................................................................... 37
Informationsystem modelling ............................................................................................................................. 37
College 11: BPM advanced modeling + identification + discovery .................................................................. 44
Process discovery, identification, and advanced modelling .............................................................................. 44
College 12: BPM Redesign ................................................................................................................................... 46
Redesign heuristics ............................................................................................................................................. 46
Devil’s quadrangle ............................................................................................................................................. 46
College 13: Bisimulatie ......................................................................................................................................... 47
Strong Bisimulation ............................................................................................................................................ 47
College 15: Quality Assurance (design and modelling rules) ........................................................................... 50
Syntactic quality ................................................................................................................................................. 50
Semantic quality ................................................................................................................................................. 50
Pragmatic quality ............................................................................................................................................... 50
Process modelling guidelines (7PMG)............................................................................................................... 52
College 16: Net properties & coverability .......................................................................................................... 54
Net properties ..................................................................................................................................................... 54
Coverability graph ............................................................................................................................................. 56
College 17: Coverability graph maken ............................................................................................................... 57
College 18: BPMN Analysis ................................................................................................................................. 60
College 19: Structuureigenschappen van Petri netten ...................................................................................... 61
Plaats invarianten .............................................................................................................................................. 61
Transitie invarianten .......................................................................................................................................... 66
2
,College 1: Labeled Transitie Systemen
Behandelde stof: [1] Hoofdstuk 1 en 4
How do we model behavior?
Mathmatical notations
Q: set of states
A: set of actions
à Q x Av{t} x Q
Set of transitions
Intitial state
3 mogelijke opties
Waar is het model voor bedoeld? Geen van de drie is een goed antwoord.
3
, In this example: C = {1,2,3,4} and D = {3,4,5}
Symbol Meaning Example
{} Set: a collection of elements {1,2,3,4}
A∪B Union: in A or B (or both) C ∪ D = {1,2,3,4,5}
A∩B Intersection: in both A and B C ∩ D = {3,4}
A⊆B Subset: A has some (or all) elements of B {3,4,5} ⊆ D
A⊂B Proper Subset: A has some elements of B {3,5} ⊂ D
A⊄B Not a Subset: A is not a subset of B {1,6} ⊄ C
A⊇B Superset: A has same elements as B, or more {1,2,3} ⊇ {1,2,3}
A⊃B Proper Superset: A has B's elements and more {1,2,3,4} ⊃ {1,2,3}
A⊅B Not a Superset: A is not a superset of B {1,2,6} ⊅ {1,9}
Ac Complement: elements not in A Dc = {1,2,6,7}
When = {1,2,3,4,5,6,7}
A−B Difference: in A but not in B {1,2,3,4} − {3,4} = {1,2}
a∈A Element of: a is in A 3 ∈ {1,2,3,4}
b∉A Not element of: b is not in A 6 ∉ {1,2,3,4}
∅ Empty set = {} {1,2} ∩ {3,4} = Ø
Universal Set: set of all possible values
(in the area of interest)
P(A) Power Set: all subsets of A P({1,2}) = { {}, {1}, {2}, {1,2} }
A=B Equality: both sets have the same members {3,4,5} = {5,3,4}
A×B Cartesian Product {1,2} × {3,4}
(set of ordered pairs from A and B) = {(1,3), (1,4), (2,3), (2,4)}
|A| Cardinality: the number of elements of set A |{3,4}| = 2
| Such that { n | n > 0 } = {1,2,3,...}
: Such that { n : n > 0 } = {1,2,3,...}
∀ For All ∀x>1, x2>x
∃ There Exists ∃ x | x2>x
∴ Therefore a=b b=a
N Natural Numbers {1,2,3,...} or {0,1,2,3,...}
Z Integers {..., -3, -2, -1, 0, 1, 2, 3, ...}
Q Rational Numbers
A Algebraic Numbers
R Real Numbers
I Imaginary Numbers 3i
C Complex Numbers 2 + 5i
4
SA M E N VAT T I N G
+,-.-+,+,
I N H O U D S O P G AV E
College 1: Labeled Transitie Systemen ................................................................................................................. 3
College 2: Grafen doorzoeken ............................................................................................................................... 7
2.1 Breadth First Search ...................................................................................................................................... 7
2.2 Depth First Search ......................................................................................................................................... 8
2.3 Dijkstra’s shortest path algorithm ................................................................................................................. 9
College 3: Informatiemodellen ............................................................................................................................ 11
It’s a True World ................................................................................................................................................ 11
College 4: BPM (I) ................................................................................................................................................ 15
Ingrediënten van het BPMN-proces ................................................................................................................... 15
BPM-lifecycle: .................................................................................................................................................... 15
College 5: Synchroon Product en Inleiding Petrinetten .................................................................................... 16
5.1 Synchroon product ....................................................................................................................................... 16
5.2 Using The Synchronous Product in modeling .............................................................................................. 18
5.3 Informal Introduction to Petri Nets .............................................................................................................. 20
5.4 Modeling with Petri Nets.............................................................................................................................. 20
College 6: Modeling with Petri Nets.................................................................................................................... 22
6.1 Formal Definition of Petri Nets.................................................................................................................... 22
6.2 Extending Petri Nets with Arc Weights ........................................................................................................ 24
College 7: Bpm-basic modelling .......................................................................................................................... 25
BPMN vertalen naar Petri net............................................................................................................................ 25
College 8: Petrinetten III...................................................................................................................................... 26
8.1 Reachability Graphs and Petri nets ............................................................................................................. 26
8.2 Petri Net Classes .......................................................................................................................................... 28
College 9: Petrinetten met Data........................................................................................................................... 33
9.1 Colored Petri nets ........................................................................................................................................ 33
, 9.2 Petri nets with identifiers ............................................................................................................................. 34
College 10: Informatiesysteemmodelleren ......................................................................................................... 37
Informationsystem modelling ............................................................................................................................. 37
College 11: BPM advanced modeling + identification + discovery .................................................................. 44
Process discovery, identification, and advanced modelling .............................................................................. 44
College 12: BPM Redesign ................................................................................................................................... 46
Redesign heuristics ............................................................................................................................................. 46
Devil’s quadrangle ............................................................................................................................................. 46
College 13: Bisimulatie ......................................................................................................................................... 47
Strong Bisimulation ............................................................................................................................................ 47
College 15: Quality Assurance (design and modelling rules) ........................................................................... 50
Syntactic quality ................................................................................................................................................. 50
Semantic quality ................................................................................................................................................. 50
Pragmatic quality ............................................................................................................................................... 50
Process modelling guidelines (7PMG)............................................................................................................... 52
College 16: Net properties & coverability .......................................................................................................... 54
Net properties ..................................................................................................................................................... 54
Coverability graph ............................................................................................................................................. 56
College 17: Coverability graph maken ............................................................................................................... 57
College 18: BPMN Analysis ................................................................................................................................. 60
College 19: Structuureigenschappen van Petri netten ...................................................................................... 61
Plaats invarianten .............................................................................................................................................. 61
Transitie invarianten .......................................................................................................................................... 66
2
,College 1: Labeled Transitie Systemen
Behandelde stof: [1] Hoofdstuk 1 en 4
How do we model behavior?
Mathmatical notations
Q: set of states
A: set of actions
à Q x Av{t} x Q
Set of transitions
Intitial state
3 mogelijke opties
Waar is het model voor bedoeld? Geen van de drie is een goed antwoord.
3
, In this example: C = {1,2,3,4} and D = {3,4,5}
Symbol Meaning Example
{} Set: a collection of elements {1,2,3,4}
A∪B Union: in A or B (or both) C ∪ D = {1,2,3,4,5}
A∩B Intersection: in both A and B C ∩ D = {3,4}
A⊆B Subset: A has some (or all) elements of B {3,4,5} ⊆ D
A⊂B Proper Subset: A has some elements of B {3,5} ⊂ D
A⊄B Not a Subset: A is not a subset of B {1,6} ⊄ C
A⊇B Superset: A has same elements as B, or more {1,2,3} ⊇ {1,2,3}
A⊃B Proper Superset: A has B's elements and more {1,2,3,4} ⊃ {1,2,3}
A⊅B Not a Superset: A is not a superset of B {1,2,6} ⊅ {1,9}
Ac Complement: elements not in A Dc = {1,2,6,7}
When = {1,2,3,4,5,6,7}
A−B Difference: in A but not in B {1,2,3,4} − {3,4} = {1,2}
a∈A Element of: a is in A 3 ∈ {1,2,3,4}
b∉A Not element of: b is not in A 6 ∉ {1,2,3,4}
∅ Empty set = {} {1,2} ∩ {3,4} = Ø
Universal Set: set of all possible values
(in the area of interest)
P(A) Power Set: all subsets of A P({1,2}) = { {}, {1}, {2}, {1,2} }
A=B Equality: both sets have the same members {3,4,5} = {5,3,4}
A×B Cartesian Product {1,2} × {3,4}
(set of ordered pairs from A and B) = {(1,3), (1,4), (2,3), (2,4)}
|A| Cardinality: the number of elements of set A |{3,4}| = 2
| Such that { n | n > 0 } = {1,2,3,...}
: Such that { n : n > 0 } = {1,2,3,...}
∀ For All ∀x>1, x2>x
∃ There Exists ∃ x | x2>x
∴ Therefore a=b b=a
N Natural Numbers {1,2,3,...} or {0,1,2,3,...}
Z Integers {..., -3, -2, -1, 0, 1, 2, 3, ...}
Q Rational Numbers
A Algebraic Numbers
R Real Numbers
I Imaginary Numbers 3i
C Complex Numbers 2 + 5i
4
