<p>The authors consider the property of detectability of discrete event systems in the presence of sensor attacks in the context of cyber-security. The authors model the system using an automaton and study the general notion of detectability where a given set of state pairs needs to be (eventually or periodically) distinguished in any estimate of the state of the system. The authors adopt the ALTER sensor attack model from previous work and formulate four notions of CA-detectability in the context of this attack model based on the following attributes: strong or weak; eventual or periodic. The authors present verification methods for strong CA-detectability and weak CA-detectability. The authors present definitions of strong and weak periodic CA-detectability that are based on the construction of a verifier automaton called the augmented CA-observer. The development also resulted in relaxing assumptions in prior results on D-detectability, which is a special case of CA-detectability.</p>