This paper presents a complete account of positive and negative results on the finite axiomatizability of weak complete simulation semantics over the language BCCSP. We offer finite (un)conditional ground-complete axiomatizations for the weak complete simulation precongruence. In sharp contrast to this positive result, we prove that, in the presence of at least one observable action, the (in)equational theory of the weak complete simulation precongruence over BCCSP does not have a finite (in)equational basis. In fact, the set of (in)equations in at most one variable that hold in weak complete simulation semantics over BCCSP does not have an (in)equational basis of ‘bounded depth’, let alone a finite one.
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