On the composition and decomposition of datalog program mappings

Abstract

The purpose of this thesis is to study the composition of datalog mappings in order to analyze the situation where a sequence of datalog program queries are evaluated serially. Four related topics are investigated and shown to be useful for the optimization of datalog programs. First, the problem of when a composition mapping is equivalent to a datalog mapping (composability) is considered. An algebraic structure called composition system is abstracted from datalog mappings, and used to establish three characterizations for composability. Several consequences of these characterizations, including invariance properties of composability, are presented. Second, the reverse process of composition, namely decomposition, is examined. A canonical decomposition into (usually) smaller programs is given, as well as the decomposition of strongly linear programs and bounded programs into single-rule programs. Third, the class of prime programs is introduced and then scrutinized. Major results include the primality of a class of single-rule programs called symmetric; the existence of arbitrarily large primes; the factorization of bounded programs into single-rule primes; and a condition for the uniqueness of factorizations into primes. And fourth, a structure called datalog module is investigated in order to understand the infinite set of compositions of mappings formed from a finite set of programs. The family of datalog modules is shown to be a composition system. Finally, a special class of datalog modules, called derivation-bounded, is introduced and proven to have efficient computation and storage features. (Copies available exclusively from Micrographics Department, Doheny Library, USC, University Park, Los Angeles, CA 90089-0182.)