Undecidability of static analysis

Static analysis of programs is indispensable to any software tool, environment, or system that requires compile-time information about the semantics of programs. With the emergence of languages like C and LISP, static analysis of programs with dynamic storage and recursive data structures has become a field of active research. Such analysis is difficult, and the static-analysis community has recognized the need for simplifying assumptions and approximate solutions. However, even under the common simplifying assumptions, such analyses are harder than previously recognized. Two fundamental static-analysis problems are may alias and must alias . The former is not recursive (is undecidable), and the latter is not recursively enumerable (is uncomputable), even when all paths are executable in the program being analyzed for languages with if statements, loops, dynamic storage, and recursive data structures.