# Normalization of linear recursions based on graph transformations

• Xiaoyong Du
• Naohiro Ishii
Invited Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1006)

## Abstract

In this paper, we propose a new approach to generate normal form formulas for linear recursions based on graph transformations. We first extend the graph model proposed in [17] for representing linear recursive definitions completely, coupling with graph equivalence definitions. The new graph model is called IE-graph. Then three basic equivalence-preserving graph transformation techniques are newly defined on IE-graphs: (1) realigning; (2) reducing; (3) expanding. Based on these graph transformation techniques, we show that a general IE-graph can always be transformed equivalently into a set of disjoint unit cycles, called Normal IE-graph. The formula generated by our method is more efficient than that generated by Han and Zeng's method [7], because the formula generated by our method contains usually less variables in the recursive predicate.

## Key words

deductive databases linear recursions compilation and optimization normalization

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