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This is mandatory for complexity classes using less than linear time.

When talking about complexity classes, a worst case scenario is usually assumed.

Currently the main focus of the program is on algebraic complexity classes.

Several natural complexity classes are known to be low for themselves.

Of course, some complexity classes have complex definitions that do not fit into this framework.

Thus there are pairs of complexity classes such that one is properly included in the other.

Many complexity classes are defined using the concept of a reduction.

This motivates the concept of a problem being hard for a complexity class.

Many known complexity classes are suspected to be unequal, but this has not been proved.

The complexity class is defined to be equal to .