Sequential reactive systems include programs and devices that work with two streams of data and convert input streams of data into output streams. Such information processing systems include controllers, device drivers, computer interpreters.e result of the operation of such computing systems are in nite sequences of pairs of events of the request-response type, and, therefore, nite transducers are most o en used as formal models for them.e behavior of transducers is represented by binary relations on in nite sequences, and so, traditional applied temporal logics (like HML, LTL, CTL, mu-calculus) are poorly suited as speci cation languages, since omega-languages, not binary relations on omega-words are used for interpretation of their formulae. To provide temporal logics with the ability to de ne properties of transformations that characterize the behavior of reactive systems, we introduced new extensions of these logics, which have two distinctive features: 1) temporal operators are parameterized, and languages in the input alphabet of transducers are used as parameters; 2) languages in the output alphabet of transducers are used as basic predicates. Previously, we studied the expressive power of new extensions Reg-LTL and Reg-CTL of the well-known temporal logics of linear and branching time LTL and CTL, in which it was allowed to use only regular languages for parameterization of temporal operators and basic predicates. We discovered that such a parameterization increases the expressive capabilities of temporal logic, but preserves the decidability of the model checking problem. For the logics mentioned above, we have developed algorithms for the veri cation of nite transducers. At the next stage of our research on the new extensions of temporal logic designed for the speci cation and veri cation of sequential reactive systems, we studied the veri cation problem for these systems using the temporal logic Reg-CTL*, which is an extension of the Generalized Computational Tree Logics CTL*. In this paper we present an algorithm for checking the satis ability of Reg-CTL* formulae on models of nite state transducers and show that this problem belongs to the complexity class ExpSpace.