Inferring Expected Runtimes of Probabilistic Integer Programs Using Expected Sizes

Meyer, Fabian; Hark, Marcel; Giesl, Jürgen

doi:10.26226/morressier.604907f41a80aac83ca25cf4

2021

DOI: 10.26226/morressier.604907f41a80aac83ca25cf4

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Inferring Expected Runtimes of Probabilistic Integer Programs Using Expected Sizes

Fabian Meyer¹,

Marcel Hark²,

Jürgen Giesl³

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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.

show abstract

Latticed k-Induction with an Application to Probabilistic Programs

Batz

Chen

Kaminski

et al. 2021

Computer Aided Verification

View full text Add to dashboard Cite

show abstract

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Inferring Expected Runtimes of Probabilistic Integer Programs Using Expected Sizes

Cited by 1 publication

References 54 publications

Latticed k-Induction with an Application to Probabilistic Programs

Latticed k-Induction with an Application to Probabilistic Programs

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