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AC

2015

Springer

2015

Springer

A fundamental problem in computer science is, stated informally: Given a problem, how hard is it?. We measure hardness by looking at the following question: Given a set A whats is the fastest algorithm to determine if “x ∈ A?” We measure the speed of an algorithm by how long it takes to run on inputs of length n, as a function of n. For example, sorting a list of length n can be done in roughly n log n steps. Obtaining a fast algorithm is only half of the problem. Can you prove that there is no better algorithm? This is notoriously diﬃcult; however, we can classify problems into complexity classes where those in the same class are of roughly the same complexity. In this chapter we deﬁne many complexity classes and describe natural problems that are in them. Our classes go all the way from regular languages to various shades of undecidable. We then summarize all that is known about these classes.

Related Content

Added |
27 Mar 2016 |

Updated |
27 Mar 2016 |

Type |
Journal |

Year |
2015 |

Where |
AC |

Authors |
William I. Gasarch |

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