Logic of Programs 1979: Logic of Programs pp 145-168 | Cite as

On the algorithmic theory of dictionaries

  • Amdrzej Salwicki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 125)


A class of algebraic structures called dictionaries is defined. Among the properties (axioms) of dictionaries we find the algorithmic property : for every s the program while empty(s) do s := delete(amember(s),s) terminates. Starting with this observation we define and develop the algorithmic theory of dictionaries ATD. We are proving the representation theorem: every dictionary structure is isomorphic to the family of all finite subsets of some set. The complexity of the set of theorems of various extensions of ATD can vary from a hiperarithmetical set to the complement of a recursively enumerable set.


Representation Theorem Priority Queue Algorithmic Logic Algorithmic Theory Abstract Data Type 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Amdrzej Salwicki
    • 1
    • 2
  1. 1.Mathematical InstitutePolish Academy of SciencesWarsawPoland
  2. 2.Institute of InformaticsUniversity of WarsawWarsaw, PKiN 8 fl.Poland

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