It is interesting to point out that for these complexity classes, an increase of a constant factor on the time or the space bounds does not change the complexity classes. The reason is that a TM with a larger alphabet set and a larger set of states can simulate, in one move, a constant number of moves of a TM with a smaller alphabet set and a smaller number of states. We only show these properties for deterministic complexity classes.

#### Proposition 1.12

*Proof*

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