Wireless communication systems are inherently vulnerable to adversarial attacks since malevolent jammers might jam and disrupt the legitimate transmission intentionally. Accordingly it is of crucial interest for the legitimate users to detect such adversarial attacks. This paper develops a detection framework based on Turing machines and studies the detectability of adversarial attacks. Of particular interest are so-called denial-of-service attacks in which the jammer is able to completely prevent any transmission. It is shown that there exists no Turing machine which can detect such an attack and consequently there is no algorithm that can decide whether or not such a denialof-service attack takes place, even if there are no limitations on computational complexity and computing capacity of the hardware.