Communication systems are delicate to deliberate jamming, which may ruin legitimate communication. Two kinds of jammers exist: partial knowledge and full knowledge jammers. Jammers with partial knowledge only know the encoding and decoding functions, whereas jammers with full knowledge also know the actual message. This paper studies the detectability of Denial of Service (DoS) attacks by jammers with partial knowledge. The theoretical framework that characterizes the detectability of a DoS attack is expressed in the literature for Turing machines with no computing capacity scarcity. Even though there is no computational limitation for Turing machines, they cannot decide if a DoS attack is possible. Conversely, by following the theoretical framework, Turing machines can recognize an Arbitrarily Varying Channel (AVC) which a DoS attack is not possible. In these circumstances, we present an algorithm that detects the scenarios where DoS attack is impossible. We provide a complexity analysis and perform Monte Carlo simulations to investigate the performance of the proposed algorithm in terms of time consumption. We observe that the simulation results are compatible with the complexity analysis.