• Doron A. Peled
Part of the Texts in Computer Science book series (TCS)


Software reliability methods are based on mathematical principles. It is usually not necessary for users of these methods to master the relevant mathematical theories. In this book we are going to present both the techniques and some of the principles comprising them. We will thus necessarily use some mathematical terminology. This chapter surveys some concepts and theories that are used later in the book. Having a prior knowledge of basic notions from set theory, graph theory, complexity theory and computability is sufficient to allow the reader to skip this chapter.


Turing Machine Complexity Class Complexity Measure Exponential Complexity Empty String 
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Further Reading

Textbooks on set theory include:

  1. P. R. Halmos, Naive Set Theory, Springer-Verlag, 1987.Google Scholar
  2. K. Devlin, The Joy of Sets: Fundamentals of Contemporary Set Theory, 2nd edition, Springer-Verlag, 1993.Google Scholar

Books on graph theory include:

  1. R. Diestel, Graph Theory, Springer-Verlag, 2nd edition, 2000.Google Scholar
  2. A. Gibbons, Algorithmic Graph Theory, Cambridge University Press, 1985.Google Scholar

Books on computability and complexity theory include:

  1. J. E. Hoperoft, J. D. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, 1979.Google Scholar
  2. H. R. Lewis, Ch. Papadimitiou, Elements of the Theory of Computation, Prentice-Hall, 2nd edition, 1997.Google Scholar
  3. Ch. Papadimitiou, Computational Complexity, Addison-Wesley, 1994.Google Scholar
  4. M. Sipser, Introduction to the Theory of Computation, PWS, 1996.Google Scholar

Copyright information

© Lucent Technologies 2001

Authors and Affiliations

  • Doron A. Peled
    • 1
  1. 1.Computing SciencesBell Labs/Lucent TechnologiesMurray HillUSA

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