High-level Counterexamples for Probabilistic Automata

Abstract

Abstract. Providing compact and understandable counterexamples for violated system properties is an essential task in model checking. Existing works on counterexamples for probabilistic systems so far computed either a large set of system runs or a subset of the system's states, both of which are of limited use in manual debugging. Many probabilistic systems are described in a guarded command language like the one used by the popular model checker PRISM. In this paper we describe how a smallest possible subset of the commands can be identified which together make the system erroneous. We additionally show how the selected commands can be further simplified to obtain a well-understandable counterexample.

Leveraging Weighted Automata in Compositional Reasoning about Concurrent Probabilistic Systems

“…Currently, our PRISM-based implementation receives a finite set of paths as weighted witnesses to M |= P ≤p [ψ]. Generally, weighted witnesses to M |= P p[ψ] where ∈ {<, ≤} are represented as graphs with strongly connected components [41,42]. We plan to generalize transition contributions to select counterexamples from spurious weighted witnesses with strongly connected components.…”

“…A weighted witness [23,41,42] to M |= P ≤p [ψ] is a pair (σ, c) where σ ∈ Adv M is an adversary with p σ s (ψ) > p, and c is a set of finite paths in M σ such that (1) for all π ∈ c, π |= ψ; (2) for all proper prefix π of π, π |= ψ; and (3) Wt(c) > p. Observe that the set c is prefix containment free. Hence Wt(c) is well-defined.…”

Leveraging Weighted Automata in Compositional Reasoning about Concurrent Probabilistic Systems

“…It is however not recommended when M is composed of concurrent MDP's. Since the construction of the composition can be very expensive, the computation should where ∈ {<, ≤} are represented as graphs with strongly connected components [41,42]. We plan to generalize transition contributions to select counterexamples from spurious weighted witnesses with strongly connected components.…”

On Abstraction of Probabilistic Systems

“…Several approaches [48,2,30] revolve around the identification of a small subsystem of the concrete model that already violates the property. Recently, [49] showed how to characterize and compute counterexamples in terms of the commands of a probabilistic program. Despite this progress, it is yet unclear how to use these sophisticated counterexample representations for the purpose of CEGAR.…”