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 +介绍为在验证程序是BSS-Machine时承认真实的交互式协议的语言类别。 让BIR子R +（RESP。BIP SUB RX）其限制只有在谚语和Verfier之间交换布尔消息时。 我们证明了类BIP子R +和PAR子R +，并行多项式时间中Cccept的语言类别一致。 在乘法下的机器的情况下，我们表明了BIP子RX PAR子RX。 我们还通过展示一种语言L在PAR子RX中的语言L，但在IP子R +中将BIP SUB r分开了两个模型中的BIP子R。 结果，我们表明，在PAR子RX中无法解决贵金量取消，并且所有布尔语言都处于IP子RX中。
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