Loop Variant

Loop Variant

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In computer science, a loop variant is a mathematical function defined on the state space of a computer program whose value is monotonically decreased with respect to a well-founded relation by the iteration of a while loop under some invariant conditions, thereby ensuring its termination. A loop variant whose range is restricted to the non-negative integers is also known as a bound function, because in this case it provides a trivial upper bound on the number of iterations of a loop before it terminates. In general, however, the smallest set sufficient to represent the range of any loop variant that might be useful in a termination proof is an ordinal number at least 1CK, but no more than 1. The existence of a variant proves the termination of a while loop in a computer program by well-founded descent. A basic property of a well-founded relation is that it has no infinite descending chains. Therefore a loop possessing a variant will terminate after a finite number of iterations, as long as its body terminates each time.
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Product details

  • Paperback | 84 pages
  • 152 x 229 x 5mm | 136g
  • United States
  • English
  • 6136587718
  • 9786136587714