Linearization of nonlinear recursive rules

The problem of converting a simple nonlinear recursive logic query into an equivalent linear one is considered. A general method is given to transform a nonlinear rule into a sequence of linear ones. For efficient processing it is necessary to convert a nonlinear rule into a single linear rule. For such a conversion, a necessary and sufficient condition is provided for a type of doubly recursive rule to be equivalent to the resulting linear rule. It is also shown that a restricted type of higher order recursive rule is equivalent to the linear rule obtained by its conversion