# Linear speedup theorem

In computational complexity theory, the **linear speedup theorem** for Turing machines states that given any real *c > 0* and any *k*-tape Turing machine solving a problem in time *f(n)*, there is another *k*-tape machine that solves the same problem in time at most *f(n)/c + 2n + 3*, where *k>1*
.[1][2]
If the original machine is non-deterministic, then the new machine is also non-deterministic.
The concrete constants *2* and *3* in *2n+3* can be lowered, for example, to *n+2*.[1]

## References

- Christos Papadimitriou (1994). "2.4. Linear speedup".
*Computational Complexity*. Addison-Wesley. - Thomas A.Sudkamp (1994). "14.2 Linear Speedup".
*Languages and Machines: An Introduction to the Theory of Computer Science*. Addison-Wesley.

This article is issued from
Wikipedia.
The text is licensed under Creative
Commons - Attribution - Sharealike.
Additional terms may apply for the media files.