We initiate the study of verification power Affine finite automata (AfA) as a part Arthur-Merlin (AM) proof systems. show that every unary language is verified by real-valued AfA verifier. Then, we focus on verifiers restricted to have only integer-valued or rational-valued transitions. observe can be simulated verifiers, and their protocols in nondeterministic polynomial time. this upper bound...

finite affine groups are given by groups of translations and di-lations on finite cyclic groups. for cyclic groups of prime orderwe develop a time-scale (wavelet) analysis and show that for alarge class of non-zero window signals/vectors, the generatedfull cyclic wavelet system constitutes a frame whose canonicaldual is a cyclic wavelet frame.

the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}(2^5{:}s_{6})$ of $a(4)$ of index $63$‎.