We describe the design of (several variants of) a local parallel model-checking algorithm for the alternation-free fragment of the μ-calculus. It exploits a characterisation of the problem for this fragment in terms of two-player games. For the corresponding winner, our algorithm determines in parallel a winning strategy, which may be employed for debugging the underlying system interactively, and is designed to run on a network of workstations. Depending on the variant, its complexity is linear or quadratic. A prototype implementation within the verification tool Truth shows promising results in practice.
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