Top-down Decomposition Research Articles

Top-down synthesis of divide-and-conquer algorithms

A top-down method is presented for the derivation of algorithms from a formal specification of a problem. This method has been implemented in a system called cypress. The synthesis process involves the top-down decomposition of the initial specification into a hierarchy of specifications for subproblems. Synthesizing programs for each of these subproblems results in the composition of a hierarchically structured program. The initial specification is allowed to be partial in that some or all of the input conditions may be missing. cypress completes the specification and produces a totally correct applicative program. Much of cypress' knowledge comes in the form of ‘design strategies’ for various classes of algorithms. The structure of a class of divide-and-conquer algorithms is explored and provides the basis for several design strategies. Detailed derivations of mergesort and quicksort algorithms are presented.

Abstraction hierarchies in top-down design

This paper describes a program design discipline that has successfully produced well-modularized programs. The basic approach is to apply, in a uniform way, the concepts of data and procedural abstraction in a top-down decomposition during the initial programming-in-the-large phase of construction. This combination of data and procedural abstraction, called hybrid abstraction, views the system as composed almost entirely of abstract objects. The resulting structural design is partially expressed as a syntactic specification for a set of modules (a module being a set of objects) having no directly shared global data. In addition to the syntactic specification, the design expresses the abstract type decomposition and the structural relationships of the modules. Three relations on the set of modules define the hierarchies is called by, implements, and obtains resources from. These relations define the discipline and characterize the class of designs possible. Modules in practice are used in two different ways: single-instance use and multiple-instance use. Abstract objects can be of two different kinds: collection objects and singular objects. The relationships of these variations in module construction are illustrated. Three moderately large examples are shown. euclid is used to illustrate the discipline.