A game-based framework for CTL counterexamples and 3-valued abstraction-refinement

Sharon Shoham*, Orna Grumberg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This work exploits and extends the game-based framework of CTL model checking for counterexample and incremental abstraction-refinement. We define a game-based CTL model checking for abstract models over the 3-valued semantics, which can be used for verification as well as refutation. The model checking process of an abstract model may end with an indefinite result, in which case we suggest a new notion of refinement, which eliminates indefinite results of the model checking. This provides an iterative abstraction-refinement framework. This framework is enhanced by an incremental algorithm, where refinement is applied only where indefinite results exist and definite results from prior iterations are used within the model checking algorithm. We also define the notion of annotated counterexamples, which are sufficient and minimal counterexamples for full CTL. We present an algorithm that uses the game board of the model checking game to derive an annotated counterexample in case the examined system model refutes the checked formula.

Original languageEnglish
Article number1
JournalACM Transactions on Computational Logic
Issue number1
StatePublished - 1 Dec 2007
Externally publishedYes


  • 3-valued semantics
  • Abstraction-refinement
  • CTL
  • Counterexamples
  • Model checking games
  • Temporal logic


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