On the Kolmogorov expressive power of boolean query languages
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We develop a Kolmogorov complexity based tool to measure expressive power of query languages over finite structures. It works for sentences (i.e., boolean queries), and gives a meaningful definition of the expressive power of a query language in a single finite model.
The notion of Kolmogorov expressive power of a boolean query language L in a finite model A is defined by considering two values: the Kolmogorov complexity of the isomorphism type of A, equal to the length of the shortest binary description of this type, and the number of bits of this description that can be reconstructed from truth values of all queries from L in A. The closer is the second value to the first, the more expressive is the query language. After giving the definitions and proving that they are correct, we concentrate our efforts on first order logic and its powerful extensions: inflationary fixpoint logic and partial fixpoint logic. We explore some connections between the proposed Kolmogorov expressive power of boolean queries in these languages and their standard expressive power. We show that, except of being of interest for its own, our notion may have important diagnostic value for database query optimisation.
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