Verifying Communicating Multi-pushdown Systems via Split-Width

Communicating multi-pushdown systems model networks of multi-threaded recursive programs communicating via reliable FIFO channels. Hence their verification problems are undecidable in general. The behaviours of these systems can be represented as directed graphs, which subsume both Message Sequence Charts and nested words. We extend the notion of split-width to these graphs, defining a simple algebra to compose/decompose these behaviours using two natural operations: shuffle and merge. We obtain simple, uniform and optimal decision procedures for various verification problems parametrized by split-width, ranging from reachability to model-checking against MSO, PDL and Temporal Logics.

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