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Induction, Strings, and Languages

  • Michael A. Arbib
  • A. J. Kfoury
  • Robert N. Moll
Part of the Texts and Monographs in Computer Science book series (MCS)

Abstract

One of the most powerful ways of proving properties of numbers, data structures, or programs is proof by induction. And one of the most powerful ways of defining programs or data structures is by an inductive definition, also referred to as a recursive definition. Section 2.1 provides a firm basis for these principles by introducing proof by induction for the set N of natural numbers and then looking at the recursive definition of numerical functions. Words are strings of letters and numbers are strings of digits, and in Section 2.2 we look at the set of strings over an arbitrary set, stressing how induction over the length of strings may be used for both proofs and definitions. We also introduce the algebraic notion of “semiring” which plays an important role in our study of graphs in Section 6.2.

Keywords

Induction Step Basis Step Empty String Commutative Monoid Recursive Definition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1981

Authors and Affiliations

  • Michael A. Arbib
    • 1
  • A. J. Kfoury
    • 2
  • Robert N. Moll
    • 1
  1. 1.Department of Computer and Information ScienceUniversity of MassachusettsAmherstUSA
  2. 2.Department of MathematicsBoston UniversityBostonUSA

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