Mechanical analysis of program complexity

There has been a great deal of research done which investigates the problem of evaluating the complexity of particular algorithms; little effort however has been applied to the mechanization of this evaluation. This paper presents the ACE (for Automatic Complexity Evaluator) system which is able to analyse reasonably large programs like sorting programs or numerical programs in a fully mechanical way. A complexity function is derived from the initial program. This function is then automatically transformed into its non-recursive equivalent according to MacCarthy's recursion induction principle, using a pre-defined library of recursive definitions (for example id, length, exponential ...). As the execution time is not a decidable property, this transformation will not be possible in all cases. The richer the pre-defined library is, the more likely the system is to succeed. The paper presents the reasons for mechanizing complexity calculus and the problems involved. It describes the operations performed by ACE and its implementation; limitations and further improvements are discussed in conclusion.