2014 # Counterexample Generation for Discrete-Time Markov Models: An Introductory Survey

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“…Since only with given scheduler can the MDP have probability measure, the first step is to find out the scheduler under which the specification φ is violated. As mentioned in Section II, in this case the MDP will be reduced to a DTMC and generating counterexamples in DTMC can be converted into the k shortest path problem in a directed weighted graph [18].…”

confidence: 99%

“…Since only with given scheduler can the MDP have probability measure, the first step is to find out the scheduler under which the specification φ is violated. As mentioned in Section II, in this case the MDP will be reduced to a DTMC and generating counterexamples in DTMC can be converted into the k shortest path problem in a directed weighted graph [18].…”

confidence: 99%

“…input : A DTMC model C, probabilistic specification φ output: π such that Σ N n=k+1 p n ≤ p and Σ N n=k p n > p 1 E ← {∀ω ∈ P ath Ai q0 |ω |= ϕ}; 2 P t ← Σ N n=1 P r Ai M {ω n ∈ P ath Ai q0 |ω n |= ϕ}; // Computable even if N is infinite from [18] …”

confidence: 99%

“…Consider a specification ϕ that is not satisfied by an MC or MDP M. One common definition of a counterexample is a (minimal) subset S ⊆ S of the state space such that the MC or sub-MDP induced by S still violates ϕ [1]. The intuition is, that by the reduced state space critical parts are highlighted.…”

confidence: 99%

“…Recall that the agent has restricted range of vision, see Note that for a visibility distance of 2, O i is defined for 1 ≤ i ≤ 24. Consequently, an observation z = O(s) at state s is a vector z = (z (1) , . .…”

confidence: 99%