The general adversary lower-bound is now known to characterize quantum query complexity due to breakthrough work by Reichardt et al. The same line of work also establishes connections to the span program framework to design quantum algorithms.
Many interesting quantum algorithms, including ones with exponential speed-up like Simon's algorithm and Shor's algorithm for period finding can be expressed in the quantum query model.
Is there any work showing lower-bounds for these algorithms in the general adversary model? Is there any work re-deriving Simon's or Shor's algorithms in the span-program framework?
Apparently, only quantum algorithms with polynomial speed-up, like Grover's , have been re-derived using span programs (or Belov's learning graph) framework.
There is work by Korian et al. showing lower-bounds for Simon using the polynomial method, but there is apparently no known way to translate polynomial-method lower-bounds to general adversary lower bounds.