Space and Time Hierarchies for Classes of Control Structures and Data Structures

Authors:
R. J. Lipton;S. C. Eisenstat;R. A. DeMillo
Affiliations:
Department of Computer Science, Yale University, 10 Hillhouse Ave., New Haven, CT;Department of Computer Science, Yale University, 10 Hillhouse Ave., New Haven, CT;School of Information and Computer Science, Georgia Institute of Technology, Atlanta, GA
Venue:
Journal of the ACM (JACM)
Year:
1976

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Abstract

Control structures and data structures are modeled by directed graphs. In the control case nodes represent executable statements and arcs represent possible flow of control; in the data case nodes represent memory locations and arcs represent logical adjacencies in the data structure. Classes of graphs are compared by a relation ≤S.T where G ≤S.T H if G can be embedded in H with at most a T-fold increase in distance between embedded nodes by making at most S “copies” of any node in G. For both control structures and data structures, S and T are interpreted as space and time constants, respectively. Results are presented that establish hierarchies with respect to ≤S.T for (1) data structures, (2) sequential program schemata normal forms, and (3) sequential control structures.