2014 # Minimal counterexamples for linear-time probabilistic verification

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“…Witnessing subsystems in MDPs have been considered in [6,9] and [19], which focuses on succinctly representing witnessing schedulers. The mixed integer linear programming (MILP) formulation of [76,77] allows for an exact computation of minimal witnessing subsystems for the property Pr max s0 (♦ goal) λ. NPcompleteness of computing minimal witnessing subsystems in MDPs was shown in [23], but the exact complexity has, to the best of our knowledge, not been determined for DTMCs (the problem was conjectured to be NP-complete in [76]).…”

confidence: 99%

“…Witnessing subsystems in MDPs have been considered in [6,9] and [19], which focuses on succinctly representing witnessing schedulers. The mixed integer linear programming (MILP) formulation of [76,77] allows for an exact computation of minimal witnessing subsystems for the property Pr max s0 (♦ goal) λ. NPcompleteness of computing minimal witnessing subsystems in MDPs was shown in [23], but the exact complexity has, to the best of our knowledge, not been determined for DTMCs (the problem was conjectured to be NP-complete in [76]).…”

confidence: 99%

“…Subsystems, witnesses and notions of minimality. Our definition of subsystem is essentially the same to the definition in [76,77] Intuitively, a subsystem M of M contains a subset of states of M, and a transition of M originating in a state of M remains unchanged in M or is redirected to fail (instead of explicitely redirecting to fail, sub-stochastic distributions are used in [76,77] with the same effect). We say that the states S all \S all and the transitions (s, α, t) with P(s, α, t) > 0 and P (s, α, t) = 0 have been deleted in M .…”

confidence: 99%

“…An alternative would be to use an MILP encoding like, e. g., in [11,19], and optimize towards a maximal number of available nondeterministic choices. However, in our setting it is crucial to ensure incrementality in the sense that if certain changes to the constraints are necessary this does not trigger a complete restart of the solving process.…”

confidence: 99%