Using Multiset Discrimination to Solve Language Processing Problems Without Hashing

It is generally assumed that hashing is essential to solve many language processing problems efficiently; e.g., symbol table formation and maintenance, grammar manipulation, basic block optimization, and global optimization. This paper questions this assumption, and initiates development of an efficient alternative compiler methodology without hashing or sorting. The methodology rests on efficient solutions to the basic problem of detecting duplicate values in a multiset, which we call multiset discrimination. Paige and Tarjan [22] gav e an efficient solution to multiset discrimination for detecting duplicate elements occurring in a multiset of varying length strings. The technique was used to develop an improved algorithm for lexicographic sorting, whose importance stems largely from its use in solving a variety of isomorphism problems [2]. The current paper and a related paper [23] show that full lexicographic sorting is not needed to solve these isomorphism problems, because they can be solved more efficiently using straightforward extensions to the simpler multiset discrimination technique. By reformulating language processing problems in terms of multiset discrimination, we also show how almost ev ery subtask of compilation can be solved without hashing in worst case running time no worse (and frequently better) than the best previous expected time solution (under the assumption that one hash operation takes unit expected time). Because of their simplicity, our solutions may be of practical as well as theoretical interest. The various applications presented culminate with a new algorithm to solve iterated strength reduction folded with useless code elimination that runs in worst case asymptotic time and auxiliary space Θ(|L| + |L * |), where |L| and |L * | represent the lengths of the initial and optimized programs respectively. The previous best solution due to Cocke and Kennedy takes Ω(|L||L * |) hash operations 1. A preliminary version of this paper appeared in the Conference Record of the Eighteenth Annual ACM Symposium on Principles of Programming Languages[6]. Part of this work was done while both authors were visiting the University of Wisconsin at Madison, and while R. Paige was visiting DIKU at the University of Copenhagen. 2. The research of this author was partially supported by National Science Foundation Grant No. CCR-9002428 and by Air Force Office of Scientific Research Grant No. AFOSR-91-0308. 3. The research of this author was partially supported by Office of Naval Research Grant No. N00014-93-1-1036 and by Air Force Office of Scientific Research Grant No. AFOSR-91-0308.