We introduce the lcasses IP sub R+ as the class of languages that admit an interactive protocol on the reals when the verifier is a BSS-machine with addition. Let BIR sub R+(resp. BIP sub Rx) its restriction when only boolean messages can be exchanged between the prover and the verfier. We prove that the classes BIP sub R+ and PAR sub R+, the class of languages cccepted in parallel polynomial time coincide. In the case of multiplicativve machines, we show that BIP sub Rx PAR sub Rx. We also separate BIP sub R from IP sub R in both models by exhibiting a language L which is nt in PAR sub Rx but in IP sub R+. As a consequence we show that aditive quantifier elimination can't be solved in PAR sub Rx and that all boolean languages are in IP sub Rx.
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机译：我们将lcasses IP sub R +作为一种语言类别，当验证程序是带有附加功能的BSS机器时，它会接受实际的交互式协议。当在证明方和验证方之间只能交换布尔消息时，让BIR子R +（分别是BIP子Rx）成为其限制。我们证明并行多项式时间内接受的语言类别BIP sub R +和PAR sub R +是一致的。在乘法机的情况下，我们显示BIP子Rx PAR子Rx。我们还通过在PAR sub Rx中但在IP sub R +中表现为nt的语言L，在两种模型中也将BIP sub R和IP sub R分开。结果表明，在PAR sub Rx中无法解决加性量词消除，并且所有布尔语言都在IP sub Rx中。
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