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You might say that G is the undo function of F, because it cancels all effects of applying F to a system in the state S0. It s important to note that if G is the inverse of F for a particular initial system state (S0), it doesn t necessarily follow that G is the inverse of F for all possible initial system states. When G can invert F only for a certain subset of the possible initial system states, then G is the bounded inverse of F, where the bound denotes the set of system states for which G is able to invert F. For example, if G is able to invert F only for the initial states {S0, S2}, then G is the bounded inverse of F for the set of initial states {S0, S2}. Using mathematical symbols, I ll state this using this formula: G = InverseT(F) where T = {S0, S2}

The basic statement for shrinking segments performs both phases of the segment-shrinking operation (first compacting, then resetting the HWM and releasing the space) in sequence. Here s the statement (the name of the table being shrunk is test): SQL> ALTER TABLE test SHRINK SPACE; Once you issue this command, Oracle will first compact the segment and then reset the HWM level and yield the freed space to the tablespace. Since the second phase, the resetting of the HWM, will affect DML operations, you may not want to use it when a large number of users are connected to the database. Instead, you may want to issue the following command, which only compacts the space in the segment: SQL> ALTER TABLE test SHRINK SPACE COMPACT; This way, during peak hours, the database will merely compact the space in the segment. During off-peak hours, you can issue the ALTER TABLE table_name SHRINK SPACE command, and this will finish the shrinking process by performing the second phase. If you use the CASCADE option during a segment-shrinking operation, all the dependent segments will be shrunk as well. For example, if you shrink a table, all the dependent index segments will be automatically shrunk. Here s how you specify the CASCADE option: SQL> ALTER TABLE test SHRINK SPACE CASCADE;

Using the new Segment Advisor, you can easily identify the segments that are good candidates for shrinking. The Segment Advisor bases its recommendations on the amount of fragmentation within an object. It determines whether objects have enough space to be reclaimed, taking into account the future space requirements. It bases its estimates of the future space requirements of an object on historical trends. Besides helping you select candidates for shrinking, the Segment Advisor is also helpful in sizing new database objects. The following sections describe how to use the advisor for both purposes.

You can use the Segment Advisor only for Oracle Database 10.1 and 10.2, and Oracle Database 11g Release 1 and later versions. In order to run the Segment Advisor, you must have the ADVISOR privilege in addition to the CREATE ANY JOB (or CREATE JOB) privilege.

The subscript T is the set of all initial system states for which G is the inverse of F. When G can invert F for any arbitrary initial state, then G is the unbounded inverse of G, or simply the inverse of F. An unbounded inverse of F, G can be described using this equation, where Sx is an arbitrary initial system state: G(F(Sx)) = Sx Using the Inverse function, you can also write this: G = Inverse(F)