Nested table handling by flat table operators

It is well known that nest and flat operations play an essential role in handling non-first-normal-form (NF²) relations. In addition to nest and flat, operations extending original relational algebra have been proposed for NF² relations. The authors study whether those extended relational algebra operations can be expressed as sequences of nest, flat, and original relational algebra operations. In this paper, NFR decomposition and GNFR decomposition are focused on, and conditions for the decompositions are clarified. The discussion is based on an NF² relational model, the nested table data model (NTD). In NTD, data are represented in nested tables (NTs), and algebraic operations named NT operations are provided. Basic properties of nest, flat, and their sequences are clarified. Canonical NTs (CNTs) and normalization lossless NTs (NLNTs) are defined. Conditions for NFR decomposition based on the concept of CNT are shown. It is shown that there is no difference between conditions for NFR decomposition and GNFR decomposition, with the exception that NLNT plays the role of CNT in GNFR decomposition. The extension of such decompositions from XR operations to sequences of NT operations is discussed