Bounded model checking of infinite state systems

Schuele, Tobias; Schneider, Klaus

doi:10.1007/s10703-006-0019-9

Cited by 10 publications

(8 citation statements)

References 62 publications

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“…SAT and SMT solvers have been used for bounded model checking [7,27]. These methods use a reasoner directly for model checking by expanding the transition relation for a finite number of steps.…”

Section: Related Workmentioning

confidence: 99%

Verifying CTL-live properties of infinite state models using an SMT solver

Vakili

Day

2014

Proceedings of the 22nd ACM SIGSOFT International Symposium on Foundations of Software Engineering

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The ability to create and analyze abstract models is an important step in conquering software complexity. In this paper, we show that it is practical to verify dynamic properties of infinite state models expressed in a subset of CTL directly using an SMT solver without iteration, abstraction, or human intervention. We call this subset CTL-Live and it consists of the operators of CTL expressible using the least fixed point operator of the mu-calculus, which are commonly considered liveness properties (e.g., AF, AU). We show that using this method the verification of an infinite state model can sometimes complete more quickly than verifying a finite version of the model. We also examine modelling techniques to represent abstract models in first-order logic that facilitate this form of model checking.

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Section: Related Workmentioning

confidence: 99%

Verifying CTL-live properties of infinite state models using an SMT solver

Vakili

Day

2014

Proceedings of the 22nd ACM SIGSOFT International Symposium on Foundations of Software Engineering

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“…Beryl contains algorithms for global and local model checking, as well as bounded variants thereof [23]. There are many differences between these algorithms that may lead to fundamentally different runtimes.…”

Section: Model Checkingmentioning

confidence: 99%

“…There are many differences between these algorithms that may lead to fundamentally different runtimes. For the verification of infinite state systems, it is even more important to have different model checking algorithms, since termination cannot be guaranteed due to the undecidability of most verification problems [23].…”

Section: Model Checkingmentioning

confidence: 99%

Verifying the adaptation behavior of embedded systems

Schneider

Schuele

Trapp

2006

Proceedings of the 2006 International Workshop on Self-Adaptation and Self-Managing Systems

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Many complex embedded systems dynamically adapt their components, services, algorithms, and parameters to the environment. This leads to new classes of design errors, since adaptation has become an increasingly complex part of the systems' behavior. In particular, as adaptations often continuously trigger further adaptations in other components, inconsistent and unstable configurations may be reached. Formal verification, which is routinely applied in safety-critical applications, must therefore consider not only temporal and functional properties of a system, but also its ability to dynamically adapt itself according to external and internal stimuli.In this paper, we describe how the adaptation behavior of embedded systems can be modeled, specified, and verified at design time. The systems are thereby given at a high level of abstraction, where adaptation is triggered by the quality of data values. This allows to extract the relevant information in a form that can be directly used for verification. Moreover, we demonstrate how state-of-the-art model checkers can be used to formally reason about the resulting system description.

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“…For infinite-state systems, however, such completeness thresholds need not exist (cf. [64]), rendering BMC a refutation-only technique. To verify infinite-state systems, BMC is typically combined with the search for an inductive invariant, i.e., a superset of the reachable states which is closed under the transition relation.…”

Section: Introductionmentioning

confidence: 99%

Latticed k-Induction with an Application to Probabilistic Programs

Batz

Chen

Kaminski

et al. 2021

Computer Aided Verification

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We revisit two well-established verification techniques, k-induction and bounded model checking (BMC), in the more general setting of fixed point theory over complete lattices. Our main theoretical contribution is latticed k-induction, which (i) generalizes classical k-induction for verifying transition systems, (ii) generalizes Park induction for bounding fixed points of monotonic maps on complete lattices, and (iii) extends from naturals k to transfinite ordinals $$\kappa $$ κ , thus yielding $$\kappa $$ κ -induction.The lattice-theoretic understanding of k-induction and BMC enables us to apply both techniques to the fully automatic verification of infinite-state probabilistic programs. Our prototypical implementation manages to automatically verify non-trivial specifications for probabilistic programs taken from the literature that—using existing techniques—cannot be verified without synthesizing a stronger inductive invariant first.

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Bounded model checking of infinite state systems

Cited by 10 publications

References 62 publications

Verifying CTL-live properties of infinite state models using an SMT solver

Verifying CTL-live properties of infinite state models using an SMT solver

Verifying the adaptation behavior of embedded systems

Latticed k-Induction with an Application to Probabilistic Programs

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