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KSE 2014 October 10th, 2014 Hanoi Formalising Concurrent UML State Machines Using Coloured Petri Nets tienne Andr, Mohamed Mahdi Benmoussa, Christine Choppy Universit Paris 13, Sorbonne Paris Cit, LIPN, CNRS, France Andr, Benmoussa,

  1. KSE 2014 October 10th, 2014 Hanoi Formalising Concurrent UML State Machines Using Coloured Petri Nets Étienne André, Mohamed Mahdi Benmoussa, Christine Choppy Université Paris 13, Sorbonne Paris Cité, LIPN, CNRS, France André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 1 / 21

  2. Introduction Motivation: Complex Systems Safety Need for early bug detection Bugs discovered when final testing: expensive � Need for a thorough modelling phase Critical and complex systems that need verification Specification with UML state machines (SMDs) [OMG, 2011] Informal description of UML semantics No formal verification on UML state machines Solution: Provide a formalisation using coloured Petri nets André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 2 / 21

  3. Outline Outline Concepts (SMDs & CPNs) 1 Translation of Concurrent State Machines 2 Conclusion and Perspectives 3 André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 3 / 21

  4. Concepts (SMDs & CPNs) Outline Concepts (SMDs & CPNs) 1 Translation of Concurrent State Machines 2 Conclusion and Perspectives 3 André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 4 / 21

  5. Concepts (SMDs & CPNs) UML State Machines (SMDs) UML Behavioural State Machines Transition systems used to express the behaviour of dynamic systems Specified in [OMG, 2011] Widely used in the industry Semantics not formally expressed Informal specification in [OMG, 2011] Not directly suitable for formal methods André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 5 / 21

  6. Concepts (SMDs & CPNs) UML State Machines (SMDs) Example of a CD Player [Zhang and Liu, 2010] Features A hierarchy of simple and composite states Transitions (including inter-level) with events Entry ( find track start ) and do ( play track ) behaviours Global variables ( present and track ) History pseudostate ( H ) André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 6 / 21

  7. Concepts (SMDs & CPNs) UML State Machines (SMDs) Example of a CD Player (cont.) This example is simple Few states, few events, few variables No exit behaviour André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 7 / 21

  8. Concepts (SMDs & CPNs) UML State Machines (SMDs) Example of a CD Player (cont.) This example is simple Few states, few events, few variables No exit behaviour And still. . . Can we ensure the following? “When in PLAYING , there is a CD in the player” “When in PLAYING , the track number is always between 1 and trackCount ” André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 7 / 21

  9. Concepts (SMDs & CPNs) UML State Machines (SMDs) Example of a CD Player (cont.) This example is simple Few states, few events, few variables No exit behaviour And still. . . Can we ensure the following? “When in PLAYING , there is a CD in the player” “When in PLAYING , the track number is always between 1 and trackCount ” Not easy to guarantee! (So what about larger case studies. . . ) André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 7 / 21

  10. Concepts (SMDs & CPNs) UML State Machines (SMDs) Main Goal We translate UML state machines to coloured Petri nets (CPNs) Set of considered constructs Hierarchy of composite states simple orthogonal (with regions) Inter-level transitions Entry, do, exit behaviours with global variables History pseudostates Concurrency (fork, join, synchronization) André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 8 / 21

  11. Concepts (SMDs & CPNs) UML State Machines (SMDs) Main Goal We translate UML state machines to coloured Petri nets (CPNs) Set of considered constructs Hierarchy of composite states simple orthogonal (with regions) Inter-level transitions Entry, do, exit behaviours with global variables History pseudostates Concurrency (fork, join, synchronization) André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 8 / 21

  12. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets [Petri, 1962] A kind of automaton Bipartite graph with places and transitions Tokens can be added to places Represent data or control A state (configuration) of the Petri net: a marking Number of tokens in each place Evolves when firing transitions Initial state: initial marking Advantages of Petri nets Detailed view of the process with an expressive graphical representation A formal semantics Powerful tools to simulate and verify the model w.r.t. various properties (reachability, boundedness, invariants, deadlock-freeness, etc.) André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 9 / 21

  13. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  14. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  15. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  16. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  17. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  18. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  19. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  20. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  21. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  22. Concepts (SMDs & CPNs) Coloured Petri Nets Petri Nets: An Example A DVD renting machine Customer’s coins Earned coins DVDs available DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 10 / 21

  23. Concepts (SMDs & CPNs) Coloured Petri Nets Coloured Petri Nets [Jensen and Kristensen, 2009] Extension of Petri nets with colours Tokens and places have a type (“colour set”) Arcs are labelled with expressions Transitions can have a guard André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 11 / 21

  24. Concepts (SMDs & CPNs) Coloured Petri Nets Coloured Petri Nets [Jensen and Kristensen, 2009] Extension of Petri nets with colours Tokens and places have a type (“colour set”) Arcs are labelled with expressions Transitions can have a guard Example: A more complex version of the DVD renting machine 1’(Alice, 30 ¤ ) Legend NAMExINT ++ 1’(Bob, 20 ¤ ) Customers ( c, m ) ( c, m − p ) INT FILMxINT 2’(Satan Tango, 12 ¤ ) e [ m ≥ p ] omon, 6 ¤ ) 1’(0 ¤ ) Money earned ++ 1’(Rash¯ ( f, p ) ++ 1’(Un retour, 10 ¤ ) e + p ( f, p ) ( f, p ) DVDs available ( f, p ) FILMxINT DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 11 / 21

  25. Concepts (SMDs & CPNs) Coloured Petri Nets Coloured Petri Nets [Jensen and Kristensen, 2009] Extension of Petri nets with colours Tokens and places have a type (“colour set”) Arcs are labelled with expressions Transitions can have a guard Example: A more complex version of the DVD renting machine 1’(Alice, 30 ¤ ) Legend NAMExINT ++ 1’(Bob, 20 ¤ ) Customers ( c, m ) ( c, m − p ) INT FILMxINT 2’(Satan Tango, 12 ¤ ) e [ m ≥ p ] omon, 6 ¤ ) 1’(0 ¤ ) Money earned ++ 1’(Rash¯ ( f, p ) ++ 1’(Un retour, 10 ¤ ) e + p ( f, p ) ( f, p ) DVDs available ( f, p ) FILMxINT DVDs on loan André, Benmoussa, Choppy (Paris13) Formalising UML State Machines Oct 10th, 2014 11 / 21

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