Abstract
AbstractWe revisit two well-established verification techniques,k-inductionandbounded model checking(BMC), in the more general setting of fixed point theory over complete lattices. Our main theoretical contribution islatticed k-induction, which (i) generalizes classicalk-induction for verifying transition systems, (ii) generalizes Park induction for bounding fixed points of monotonic maps on complete lattices, and (iii) extends from naturalskto transfinite ordinals$$\kappa $$κ, thus yielding$$\kappa $$κ-induction.The lattice-theoretic understanding ofk-induction and BMC enables us to apply both techniques to thefully 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.
Highlights
Bounded model checking (BMC) [12,17] is a successful method for analyzing models of hardware and software systems
This paper explores whether k-induction can have a similar impact on the fully automatic verification of infinite-state probabilistic programs
A prototypical implementation of our method demonstrates that κ-induction for probabilistic programs manages to automatically verify non-trivial specifications for programs taken from the literature which—using existing techniques—cannot be verified without synthesizing a stronger inductive invariant
Summary
Bounded model checking (BMC) [12,17] is a successful method for analyzing models of hardware and software systems. For checking a finite-state transition system (TS) against a safety property (“bad states are unreachable”), BMC unrolls the transition relation until it either finds a counterexample and refutes the property, or reaches a pre-computed completeness threshold on the unrolling depth and accepts the property as verified. For infinite-state systems, 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. A plethora of techniques target computing or approximating inductive invariants, including IC3 [14], induction [13,20], interpolation [50,51], and predicate abstraction [27,36]. Invariant synthesis may burden full automation, as it either relies on user-supplied annotations or confines push-button technologies to semi-decision or approximate procedures
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
