Abstract
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.
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© 1981 Springer-Verlag Berlin Heidelberg
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Salwicki, A. (1981). On the algorithmic theory of dictionaries. In: Engeler, E. (eds) Logic of Programs. Logic of Programs 1979. Lecture Notes in Computer Science, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11160-3_5
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DOI: https://doi.org/10.1007/3-540-11160-3_5
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