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Acta Informatica

, Volume 8, Issue 2, pp 125–144 | Cite as

Backtracking in recursive computations

  • Nissim Francez
  • Boris Klebansky
  • Amir Pnueli
Article

Summary

A mathematical (denotational) semantics is constructed for a formalism of recursive equations with the Alternative operator. This formalism enables the combination of recursion and backtracking. The semantics is defined by applying fixpoint theory to set valued functions. We introduce the notion of strategy to produce subsets of the result. Two implementations are suggested using an auxiliary stack, that trade off recomputation time with space in the auxiliary stack. The concept of a sub-fixpoint is introduced, and the implementations are shown to be incomplete even w.r.t. sub-fixpoint values. One special strategy, the leftmost strategy, which stems from problems such as pattern matching or parsing, is discussed.

Keywords

Information System Operating System Data Structure Communication Network Information Theory 
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 1977

Authors and Affiliations

  • Nissim Francez
    • 1
    • 2
  • Boris Klebansky
    • 1
  • Amir Pnueli
    • 2
  1. 1.Department of Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Department of Mathematics (Division of Computer Science)Tel Aviv UniversityTel AvivIsrael

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