Brown University Providence , Rhode Island 02912

This paper describes MEDUSA, an experimental algorithm synthesizer. MEDUSA is characterized by its top-down approach, its use of cost-constraints, and its restricted number of synthesis methods. Given this model, we discuss heuristics used to keep this process from being unbounded search through the solution space. The results indicate that the performance criteria can be used effectively to help avoid combinatorial explosion. The system has synthesized a number of algorithms in its test domain (geometric intersection problems) without operator intervention. o Synthesis should be done without user intervention Algorithms will be produced to meet some given performance constraints o The synthesizer should be reasonably efficient, i.e., it should be considerably better than exhaustive search. Algorithm synthesis in general is very difficult; it requires large amounts of domain and design knowledge, and much of design appears to be complex manipulations and intuitive leaps. We have attempted to circumvent these problems by working with a restricted set of synthesis methods in a restricted domain. The underlying hypothesis is that a fairly restricted set of methods can be used to produce algorithms with clean design and adequate (if not optimal) performance. The domain to develop and test MEDUSA is planar intersection problems from computational geometry. This domain has a number of characteristics that make it a good test area: Nearly all objects of interest are sets, so most algorithmic tasks can be defined in terms of set primitives. f This work owes a lot to the continuing support, encouragement. and advice of Eugene Char&k, and has been supported in part by the Office of Naval Research under grant N00014-79-C-0529 There exist a number of tasks that are not very hard ( i.e. linear to quadratic complexity); algorithms in this range are practical for reasonably large problems. Although all of the objects are ultimately point sets, most can be described by other composite structures (e.g. lines, planar regions), so object representation is naturally hierarchical. Problems in this domain are solvable by a variety of techniques, some general and some domain-specific. Choosing the proper technique from a number of possibilities is often necessary to obtain the desired performance. The test problems (with associated performance constraints) used in developing this system are given in table 1. These problems have many similarities (minimizing the amount of domain knowledge needed), but differ enough to demand reasonable extensibility of techniques. MEDUSA is implemented in LISP. It uses and modifies a first-order predicate calculus database using the deductive database system DUCK. [7]. The database contains knowledge about specific algorithms, general design techniques, and domain knowledge, and is used as a scratchpad during synthesis. Useful DUCK features include data dependencies, datapools, and a convenient bi-directional LISP interface.