Iterative algorithms for global flow analysis

This paper studies iterative methods for the global flow analsis of computer programs. We define a hierarchy of global flow problem classes, each solvable by an appropriate generalization of the "node listing" method of Kennedy. We show that each of these generalized methods is optimum, among all iterative algorithms, for solving problems within its class. We give lower bounds on the time required by iterative algorithms for each of the problem classes.

[1]  Jeffrey D. Ullman,et al.  Application of lattice algebra to loop optimization , 1975, POPL '75.

[2]  Arto Salomaa,et al.  Two Complete Axiom Systems for the Algebra of Regular Events , 1966, JACM.

[3]  Frances E. Allen,et al.  Control-flow analysis , 2022 .

[4]  M. Newey Notes on a problem involving permutations as subsequences. , 1973 .

[5]  R. Tarjan Solving path problems on directed graphs. , 1975 .

[6]  Daniel J. Kleitman,et al.  A Lower Bound on the Length of a Sequence Containing All Permutations as Subsequences , 1976, J. Comb. Theory, Ser. A.

[7]  Alfred V. Aho,et al.  Node listings for reducible flow graphs , 1975, STOC '75.

[8]  Donald E. Knuth,et al.  An empirical study of FORTRAN programs , 1971, Softw. Pract. Exp..

[9]  Ken Kennedy,et al.  Node listings applied to data flow analysis , 1975, POPL '75.

[10]  Robert E. Tarjan,et al.  Lower bounds on the lengths of node sequences in directed graphs , 1976, Discret. Math..

[11]  R. Backhouse,et al.  Regular Algebra Applied to Path-finding Problems , 1975 .

[12]  Jeffrey D. Ullman,et al.  Characterizations of Reducible Flow Graphs , 1974, JACM.

[13]  Ben Wegbreit,et al.  Property extraction in well-founded property sets , 1975, IEEE Transactions on Software Engineering.

[14]  Robert McNaughton,et al.  The theory of automata , 1961 .

[15]  Robert E. Tarjan,et al.  Efficiency of a Good But Not Linear Set Union Algorithm , 1972, JACM.

[16]  Mark N. Wegman,et al.  A Fast and Usually Linear Algorithm for Global Flow Analysis , 1976, J. ACM.

[17]  S C Kleene,et al.  Representation of Events in Nerve Nets and Finite Automata , 1951 .

[18]  Gary A. Kildall,et al.  A unified approach to global program optimization , 1973, POPL.

[19]  Alfred V. Aho,et al.  The Theory of Parsing, Translation, and Compiling , 1972 .

[20]  Jeffrey D. Ullman A Fast Algorithm for the Elimination of Common Subexpressions , 1972, SWAT.