Axiomatizing GSOS with Predicates

In this paper, we introduce an extension of the GSOS rule format with predicates such as termination, convergence and divergence. For this format we generalize the technique proposed by Aceto, Bloom and Vaandrager for the automatic generation of ground-complete axiomatizations of bisimilarity over GSOS systems. Our procedure is implemented in a tool that receives SOS specifications as input and derives the corresponding axiomatizations automatically. This paves the way to checking strong bisimilarity over process terms by means of theorem-proving techniques.

💡 Research Summary

This paper extends the well‑known GSOS rule format, which traditionally captures only transition behaviour, by adding a first‑class notion of predicates such as termination, convergence and divergence. The resulting formalism, called a “preg” system, allows each operational rule to contain positive and negative premises not only about actions (transitions) but also about predicates. A preg transition rule for an ℓ‑ary operator f has the shape

 { x_i ─a_ij→ y_ij | i∈I⁺, j∈I⁺_i } ∪ { P_ij x_i | i∈J⁺, j∈J⁺_i } ∪ { x_i ─b↛ | i∈I⁻, b∈B_i } ∪ { ¬Q x_i | i∈J⁻, Q∈Q_i }
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 f(x₁,…,x_ℓ) ─c→ C