Methods and apparatus are disclosed for, inter alia, managing idle time and performing lookup operations to adapt to refresh requirements and/or operational rates of the particular associative memory or other devices used to implement the system. A system typically a controller coupled to a circuit including includes multiple associative memories. The controller receives performance information from at least one of the associative memories and generates idle time corresponding to the performance information. This performance information may include an actual refresh requirement for each of the associate memories or the worst-case requirement of one of the associative memories, so that the controller can intermittently provide the actual refresh cycles required, if any, by a particular implementation. This performance information may indicate for some or all instructions the actual time required by a particular instruction, so that the controller can operate based on the actual time required, rather than inefficiently operating on a worst-case time defined in a specification or data sheet.