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The State Explosion Problem - Introduction

The State Explosion Problem - Introduction. Stephan Kugelmann Aalto University – School of Science Stephan.kugelmann@aalto.fi. Two main approaches to checking that a concurrent system is correct. Theorem proving Specially trained personnel needed

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The State Explosion Problem - Introduction

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  1. The State Explosion Problem - Introduction Stephan Kugelmann Aalto University – School of Science Stephan.kugelmann@aalto.fi

  2. Twomainapproachestocheckingthat a concurrentsystemiscorrect • Theorem proving • Speciallytrainedpersonnelneeded • Doesn‘tprovidegooddebugginginformation • State spacemethods • Incompleteanalysis. Doesn‘tprovecorrectness. • State explosion

  3. Already trivial systemscanhave a high numberofstates Dining philosophers Token ring protocol States numberofphilosophers States numberofstations http://en.wikipedia.org/wiki/File:Dining_philosophers.png

  4. Definition of State Spaces • The statespaceisdefinedasthetuple • is a setofstates. • is a setofstructuraltransitions. • is a setofsemantictransitions. • is a setofinitialstates.

  5. Semantictransitions • Formally: • Simplified(processalgebra): or • Petri nets:

  6. Sequencesofsemantictransitions

  7. Executionof a system • Finite: , Deadlocking, if last stateis a deadlock=> complete Last stateenabledstructualtransitions => incomplete • Infinite: , complete

  8. Abstractionsof States andTransitions • setof (atomic) propositions • Formally: • E.g.:“Process 2 is in itscriticalsection“ • setof observable transitionlabels • E.g.: “press_start_button“, “send_message<123>“ • a unobservableaction.

  9. Evaluation functionstodeterminethevaluesfor a statespace , newnamestostructurualtransitions. e.g. reset_x

  10. –abstractions applied on executions

  11. Stuttering, an importantissuearisingwith–abstractedexecustions forsome forsome

  12. State-basedand action-basedformalisms • Can beconvertedintoeachother • State informationencodedintoactions : and stored Alternative:

  13. Action informationencodedasstates (X,a) a a X (X,b) b b

  14. Questions?

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