This paper describes a general approach for optimized live heap space and live heap space-bound analyses for garbage-collected languages.

This paper describes a systematic method for optimizing recursive functions using both indexed and recursive data structures. The method is based on two critical ideas: first, determining a minimal input increment operation so as to compute a function on repeatedly incremented input; second, determining appropriate additional values to maintain in appropriate data structures, based on what values are needed in computation on an incremented input and how these values can be established and accessed. Once these two are determined, the method extends the original program to return the additional values, derives an incremental version of the extended program, and forms an optimized program that repeatedly calls the incremental program. The method can derive all dynamic programming algorithms found in standard algorithm textbooks. There are many previous methods for deriving efficient algorithms, but none is as simple, general, and systematic as ours.

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For memory constrained environments, optimization for program size is often as important as, if not more important than, optimization for execution speed. Commonly, compilers try to reduce the code segment but neglect the stack segment, although the stack can significantly grow during the execution of recursive functions because a separate activation record is required for each recursive call. If a formal parameter or local variable is dead at all recursive calls, then it can be declared global so that only one instance exists independent of the recursion depth. We found that in 70 % of our benchmark functions, it is possible to reduce the stack size by declaring formal parameters and local variables global. Often, live ranges of formal parameters and local variables can be split at recursive calls through program transformations. These splitting transformations allowed us to further optimize the stack size of all our benchmark functions. If all formal parameters and local variables can be declared global, then such functions may be transformable into iterations. This was possible for all such benchmark functions.