Polynomial transformation

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e: f : & # x03A3; & # x2217; & # x2192; & # x0393; & # x2217; {\displaystyle f:\Sigma ^{*}\rightarrow \Gamma ^{*}\,}

which can be calculated in polynomial time depending on the size of the input, and which is defined by: w & # x2208; L ⇔ f ( w ) & # x2208; M {\displaystyle w\in L\Leftrightarrow f(w)\in M}

for every element w of Σ.

When this function f exists, it is said that "L is polynomically transformable in M". Application The idea of ​​reducing problems in others is commonly used in classifying problems in various complexity classes, such as NP-complete, PSPACE-complete and EXPTIME-complete.

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