closure properties of IP(2pfa) and AM(2pfa)
You can take a look at the following paper:

Dwork, C. and Stockmeyer, L. 1992. Finite state verifiers I: the power of interaction. J. ACM 39, 4 (Oct. 1992), 800-828. DOI= http://doi.acm.org/10.1145/146585.146599

or the related paper:

Dwork, C. and Stockmeyer, L. 1992. Finite state verifiers II: zero knowledge. J. ACM 39, 4 (Oct. 1992), 829-858. DOI= http://doi.acm.org/10.1145/146585.146601