i am studying for a test and i have problems with the basics of mapping reductions.i can understand how to do reductions using Turing machine, but without it i get little bit confused.for example :How do I do a mapping reduction from a to b, where a is {0,1} and b is {0} over the Alphabet of {0,1}?Does every language has reduction to itself?
basic mapping reductions without using Turing machines
computation models
The identity function is a reduction from a language to itself. One reduction from $\{0,1\}$ to $\{0,1\}$ is given by $\lfloor x/2 \rfloor$, which maps $0,1$ to $0$, and all other integers to non-zero values.