Turning SOS Rules into Equations

Axiomatizing GSOS with Termination

“…• for each termination rule (j and each transition rule p for f in TS it holds that term ((j) If we consider only transition rules p with empty sets term(p) and pass(p), the notion of smooth and distinctive for the tagh-format specializes to this notion for GSOS as introduced in [ABV94]. Note that, in the absence of termination conditions, a non-active argument can be regarded as a negative one with an empty set of forbidden actions, so that the requirement for smoothness of an operation becomes trivial.…”

“…Note that, in the absence of termination conditions, a non-active argument can be regarded as a negative one with an empty set of forbidden actions, so that the requirement for smoothness of an operation becomes trivial. In [ABV94] there is another requirement for smooth operations, viz. that the negative arguments of all transition rules coincide.…”

“…The requirement of at least one active position in a smooth transition rule will be needed in our proof of the soundness of the distributive laws for negative arguments, introduced below and that are superfluous in the setting of [ABV94] but are essential for our treatment of termination (ef. Lemma 17).…”

“…In our opinion, this is due to the limited process algebraic basis employed in [ABV94]; in particular, termination and deadlock are identified. Any language, both programming and specification languages, involving some form of parallel composition will know the situation when no further action is possible, but components are not finished, e.g.…”

“…Moreover, we want two characterizations that match: the axiomatization should be sound and complete for the model of transition systems modulo (strong) bisimulation. The paper [ABV94] points the way in such an endeavour: in some cases an axiomatization can be derived by just following a recipe. Some other papers in this area are [Uli95,UliDD] (where other equivalence relations besides bisimulation equivalence are considered).…”