Relating complexity and precision in control flow analysis

We analyze the computational complexity of kCFA, a hierarchy of control flow analyses that determine which functions may be applied at a given call-site. This hierarchy specifies related decision problems, quite apart from any algorithms that may implement their solutions. We identify a simple decision problem answered by this analysis and prove that in the 0CFA case, the problem is complete for polynomial time. The proof is based on a nonstandard, symmetric implementation of Boolean logic within multiplicative linear logic (MLL). We also identify a simpler version of 0CFA related to -expansion, and prove that it is complete for logarithmic space, using arguments based on computing paths and permutations. For any fixed k > 0, it is known that kCFA (and the analogous decision problem) can be computed in time exponential in the program size. For k = 1, we show that the decision problem is NP-hard, and sketch why this remains true for larger fixed values of k. The proof technique depe...

• Type: Conference
• Year: 2007
• Where: ICFP
• Authors: David Van Horn, Harry G. Mairson
• Keywords: Analogous Decision Problem, Decision Problem, ICFP 2007, Programming Languages, Simple Decision Problem