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- W3186609013 abstract "Abstract 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 $$kappa $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>κ</mml:mi></mml:math> , thus yielding $$kappa $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>κ</mml:mi></mml:math> -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." @default.
- W3186609013 created "2021-08-02" @default.
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- W3186609013 date "2021-01-01" @default.
- W3186609013 modified "2023-10-17" @default.
- W3186609013 title "Latticed k-Induction with an Application to Probabilistic Programs" @default.
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- W3186609013 doi "https://doi.org/10.1007/978-3-030-81688-9_25" @default.
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