Basic Results of Complexity Theory

  • Steven Homer
  • Alan L. Selman
Part of the Texts in Computer Science book series (TCS)


We begin our study of complexity theory by examining the fundamental properties of complexity classes. These results apply to all complexity classes and show that the definitions of these classes are invariant under small changes in the time or space bounds of the Turing machines that define them. We will prove general relationships between time- and space-bounded complexity classes. These consist of inclusions between some classes and separations of other classes. Then we will apply the methods and results of these general relationships to important specific cases in order to establish relationships between the central standard complexity classes we defined in the previous chapter. In order to begin this study we need to understand some simple assertions that involve the behavior of functions at limits, so let’s review these now.


Turing Machine Complexity Theory Input Word Input Tape Tape Head 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Steven Homer
    • 1
  • Alan L. Selman
    • 2
  1. 1.Department of Computer ScienceBoston UniversityBostonUSA
  2. 2.Department of Computer Science and EngineeringUniversity at BuffaloBuffaloUSA

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