Heuristic Search vs. Exhaustive Search

A theorem proving system embodying a systematic search procedure is de sen bed. Al though the search spaces are usually infinite, and not even locally finite, the asymmetric way in which thev are generated results in a speed that is es 11ma-ted to be one to two orders of magnitude faster than the theorem provers of Quinlan and Hunt, and Chang and the problem-solver of Kikes, to whi c h this systern has been compared extenslvely. DescripIive terms: search, heuristic search, exhaust ive seare h , sea re h space, 1ocal1v iniIni te search space, rewri t ing ru1e, expans ion rule, theorem provi ng, problem-so1ving. 1. INTRODUCTION Heuris t i c programmi ng technl que s have been developed to make i t posslble t o solve problems whose solutions each constitute just one point or a small set of points in a very large, and possibly infinite, space, the search space. Many problems in artificial intelligence are difficult, and requi re "intelligene e" from the problem sol-ver, precisely because of the size of the search space. A 1 though heuris t ic search does not guarantee a solution, the size of the search space precludes an alternative techni que such as exhaustive search. Any me thod that would a r tempt to search unselee ti vely the whole search spat e i or a sol u-tion would qu lckly exhaus t avaliable resources of time and memory and would be bound to failure, except in some rare, "lucky" cases. The statements in the above paragraph seem so "obvi ous" that few would diSagree with them. The present study shows tha t, in fac t, they are false in regard s to severa 1 artificial intelligence systerns that have been bullt. First, the search space is very smal l in many problems, often less than even a few dozen nodes. Second, although tte search spaces may be infinite in principle, in reality only very small parts of this space need to be generated, in a systematic way, until the solution is found. Final ly, a s imple program, embodying a sys tematic, blind and "dumb" (?) procedure , was wri t ten-This program has solved over sixty problems that are typically considered as requiring heuris tic search. The vas t majority of these problems have a potentially infinite search space. An estimate of the re lative speeds of different …