Information flow properties are a way of specifying security properties of systems. A system is viewed as generating traces containing "confidential" and "visible" events (only the latter being observable by a "low-level" user) and the information flow properties specify restrictions on the kind of traces the system may generate, so as to restrict the amount of information a low-level user can infer about confidential events having taken place (or not) in an execution. Mantel identifies "basic security predicates" or BSPs and shows them to be the building blocks of most of the known trace-based properties in the literature. Traditionally BSPs have been reasoned about via unwinding conditions that capture whether a system satisfies a particular BSP. First, we show that the checking of unwinding conditions can be simplified to checking conditions on a maximal simulation relation. Second, we show that the BSPs can be characterized in terms of regularity preserving language-theoretic operations. This leads to a decision procedure for checking whether a finite state system satisfies a given BSP. Finally, we prove that the problem of verifying BSPs for pushdown systems is undecidable.