Finite Axiom Systems for Testing Preorder and De Simone Process Languages

We prove that testing preorder of De Nicola and Hennessy is preserved by all De Simone process operators. Based on this result we propose an algorithm for generating axiomatisations of testing preorder for arbitrary De Simone process languages. The axiom systems produced by our algorithm are nite and complete for processes with nite behaviour. In order to achieve completeness for a subclass of processes with innnite behaviour we use one innnitary induction rule. The usefulness of our results is illustrated in speciication and veriication of small concurrent systems, where suspension, resumption and alternation of execution of component systems occur. We argue that better speciications can be more easily written in custom-made De Simone process languages which contain both the standard operators as well as new, specially tailored for the task in hand De Simone operators. Moreover, the automatically generated axiom systems for such speciication languages make the veriication straightforward.