Useless recursion

This amounts to splitting the non-minimal case into two non-mandatory cases, called the non-recursive non-minimal case and the recursive non-minimal case, respectively. For convenience, we drop the qualifier non-minimal from these two names. Recursion may be useless in the sense that the recursively computed TY are not needed for the computation of Y. Useless recursion wouldn t affect the correctness of a logic algorithm, though. Its elimination is thus rather a matter of algorithm optimization. The following objectives of the strategy ... 

Task I In the recursive case, delete every disjunct where the general example procComp ,,yj) would have no admissible alternatives wit a = / = 1, and expand the non-recursive case wit the corresponding example Indeed, if yj is not somehow constructed in terms of tyj, then recursion is useless for testing y. 

How to detect that recursion is useless in some non-minimal sub-cases Step 4 (Syntactic introduction of the recursive atoms) creates a non-recursive case if at least one example Ej leads to a non-admissible procComp(,,yp atom. Howto invent or re-use appropriate predicates How to implement invented predicates The predicate invention problem is tackled at four points during the synthesis. At Steps 2 and 3, the Database Method re-uses predefined predicates this amounts to using domain knowledge. At Step 6, the Synthesis Method (see Section 14.2.4 below) invents new composition operators. As of now, there is no method yet of re-using common composition operators. At Step 7, the PaP Method synthesizes discriminants that are in terms of predicates other than rfn. How to discover which parameters are auxiliary parameters Due to our restriction to version 3 of the divide-and-conquer schema, auxiliary parameters are not taken into account. See Section 14.2.2 below on how to achieve this. 

This logic algorithm is totally correct wrt the intended relation. The main obstacle is the detection that recursion is useless in the second disjunct. ... 

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