Forward Analysis for WSTS, Part II: Complete WSTS

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We describe a simple, conceptual forward analysis procedure for ∞-complete WSTS \(\mathfrak S\) . This computes the clover of a state s 0, i.e., a finite description of the closure of the cover of s 0. When \(\mathfrak S\) is the completion of a WSTS \(\mathfrak X\) , the clover in \(\mathfrak S\) is a finite description of the cover in \(\mathfrak X\) . We show that this applies exactly when \(\mathfrak X\) is an ω 2 -WSTS, a new robust class of WSTS. We show that our procedure terminates in more cases than the generalized Karp-Miller procedure on extensions of Petri nets. We characterize the WSTS where our procedure terminates as those that are clover-flattable. Finally, we apply this to well-structured counter systems.