Two category spaces are defined as follows: but replacing any category c where #(c ) > k by * .
(ii) The optimistic category space of Ω given k is the pair (C Ω [k], γ +Ω ) where γ +Ω is defined like γ Ω but replacing any category c where #(c ) > k by * ; and including c ∈ γ Ω ( * ) whenever γ Ω (c) = c ; and including c ∈ γ Ω (c 1 , * ) whenever γ Ω (c 1 , c 2 ) = c ; and including c ∈ we cut off the generation of categories once their degree exceeds a user-defined threshold k. In the pessimistic (under-approximating) variant, no further combinations are possible behind * .