Off-line and on-line algorithms for deducing equalities

Authors:
Peter Downey;Hanan Samet;Ravi Sethi
Affiliations:
The Pennsylvania State University, University Park, Pennsylvania;University of Maryland, College Park, Maryland;Bell Laboratories, Murray Hill, New Jersey
Venue:
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Year:
1978

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Abstract

The classical common subexpression problem in program optimization is the detection of identical subexpressions. Suppose we have some extra information and are given pairs of expressions ei1=ei2 which must have the same value, and expressions fj1≠fj2 which must have different values. We ask if as a result, h1=h2, or h1≠h2. This has been called the uniform word problem for finitely presented algebras, and has application in theorem-proving and code optimization. We show that such questions can be answered in O(nlogn) time, where n is the number of nodes in a graph representation of all relevant expressions. A linear time algorithm for detecting common subexpressions is derived. Algorithms which process equalities, inequalities and deductions on-line are discussed.