where the summation ranges over all instantaneous expression
γ.
you need to index γ then???? you can't even make a single coherent statement about what γ is and you have no CLUE about its cardinality, even WITHIN the same timestep, let alone later???
now what is a (greek alpha in the paper)? oh yes. for that you have to scroll up to the bottom paragraph of the previous page for the densest fucking prose i have ever seen in my life:
DEFINITION.
Let Z = (U, S, p)be a PTM. An expressionaofZis a finite sequence (possibly empty) of symbols chosen fromU U S.
it's crazy how he adds "(empty set)" and "(possibly empty)" and then can't even bother to define his state indexing as another part of the fucking MACHINE STATE. and what the fuck is "of Z" about