Linearization of nonlinear recursive programs is an important issue in logic databases for both practical and theoretical reasons. If a nonlinear recursive program can be transformed into an equivalent linear recursive program, then it may be computed more efficiently than when the tranformation is not possible. We provide a set of necessary and sufficient conditions for a simple doubly recursive program to be equivalent to a simple linear recursive program. The necessary and sufficient conditions can be verified effectively.

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.>