For communication systems there is a recent trend towards shifting functionalities from the physical layer to higher layers by enabling software-focused solutions. Having obtained a (physical layer-based) description of the communication channel, such approaches exploit this knowledge to enable various services by subsequently processing it on higher layers. For this it is a crucial task to first find out in which state the underlying communication channel is. This paper develops a framework based on Turing machines and studies whether or not it is in principle possible to algorithmically decide in which state the communication system is. It is shown that there exists no Turing machine that takes the physical description of the communication channel as an input and solves a non-trivial classification task. Subsequently, this general result is used to study communication under adversarial attacks and it is shown that it is impossible to algorithmically detect denial-of-service (DoS) attacks on the transmission. Jamming attacks on ACK/NACK feedback cannot be detected as well and, in addition, ACK/NACK feedback is shown to be useless for the detection of DoS attacks on the actual message transmission.