  We initiate the study of the verification power of AfAs as part of
Arthur-Merlin (AM) proof systems. We show that every unary language is verified
by a real-valued AfA verifier. Then, we focus on the verifiers restricted to
have only integer-valued or rational-valued transitions. We observe that
rational-valued verifiers can be simulated by integer-valued verifiers, and,
their protocols can be simulated in nondeterministic polynomial time. We show
that this bound tight by presenting an AfA verifier for NP-complete problem
SUBSETSUM. We also show that AfAs can verify certain non-affine and
non-stochastic unary languages.
