The automatic verification of designs of digital circuits for their equivalence, wherein logic designs implemented in different hardware description languages and different design methodologies are compared. The device comprises an interface member capable of engaging a multiple component applicator, a body having at least two lumens therein, and a detachable spray tip in fluid communication with the body. In exemplary embodiments of the present invention additional information can be overlayed on an existing signal as a combination of amplitude and phase offset from the original QPSK symbols, applied for each information bit of the overlay data. The first unknown state may be a state that already contains the target record, or may instead be a state that does not contain the record. In one embodiment, these systems andor methods present a user interface identifying an account having a right to permit a task in response to the task being prohibited based on a user’s current account not having that right.